
LIBR ARY OF CONG RESS. 

Cllap.^^...., ^^right No., 

Shell„..X...6 

[ma 



UNITED STATES OF AMERICA. 



A NEW ASTRONOMY 



FOR BEGINNERS 



BY 



DAVID P. TODD 

M.A., PH.D. 

Professor of Astronomy and Director of the Observatory^ Amherst College 




J^. ^^^w^ 



Copyright, iSqj, by A^iterican Book Company . . ,,,,,..^ 

NEW YORK-:- CINCINNATI •:• CHICAGO 

AMERICAN BOOK COMPANY 



— ' Contouplated as one grand whole, astronomy is the most 
beautiful monument of the human jnindj the noblest record of 
its intelligence: — La Place 



Q 



^^ 



i 



%'\'i 



:iri«0 





Eo 




B. SH. 3. anti ®. dr, 3. 


in 


grateful 


memorg 


of 


' Coronet 


' tiass 



— ' The attempt to convey scientific conceptions, without the 
appeal to observation, which can alone give such conceptions 
firnniess and reality, appears to me to be in. direct aiitagonis7n 
to the fundamental principles of scientific education.'' — 
Huxley 



PREFACE 



IV TEGLECT hitherto of the adaptabiHty of astronomy to a laboratory 
^ ^ course has mainly led to the preparation of this JVew Astrononiy 
for Begiiuiers. Written purely with a pedagogic purpose, insistence 
upon rightness of principles, no matter how simple, has everywhere 
been preferred to display of mere precision in result. To instance a 
single example : although the pupiPs equipment be but a yardstick, a 
pinhole, and the 'rule of three,' \\ill he not reap greater benefit from 
measuring the sun for himself (page 259), than from learning mere 
detail of methods employed by astronomers in accurately measuring 
that luminary ? 

Astronomy is preeminently a science of observation, and there is no 
sufficient reason why it should not be so studied. Thereby will be 
fostered a habit of intellectual alertness which lets nothing slip. Six- 
teen years' experience in teaching the subject has taught me many 
lessons that I have endeavored to embody here. Earth, air, and 
water (merely material things) are always with us. We touch them, 
handle them, ascertain their properties, and experiment upon their 
relations. Plainly, in their study, laboratory courses are possible. So, 
too, is a laboratory course in astronomy, without actually journeying 
to the heavenly bodies ; for light comes from them in decipherable 
messages, and geometric truth provides the interpretation. But the 
student should learn to connect fundamental principles of astronomy 
with tangible objects of the common sort, somewhat as in phvsics and 
chemistry ; and I have aimed to indicate practically how teachers and 
pupils of moderate mechanical deftness can themselves make the appa- 
ratus requisite for illustrating many of these principles. All of it has 
been repeatedly constructed ; and its use should pave the way to better 
equipment for more advanced study. 

Especial attention has been accorded the recommendations of ' The 
Committee of Ten' on secondary school studies (1892); the specifica- 
tions concerning astronomical instiuction published by the Board of 
Regents of the state of New York (i89'5) ; and the Action of the 

3 



4 Preface 

Editorial Board of The Astrophysical Journal with regard to Standards 
in Astrophysics and Spectroscopy (1896). 

In order to secure the fullest educational value, I have aimed to 
piesent astronomy, not as mere sequence of isolated and imperfectly 
connected facts, but as an inter-related series of philosophic principles. 
The geometrical concept of the celestial sphere is strongly emphasized ; 
also its relation to astronomical instruments. But even more important 
than geometry is the philosophical correlation of geometric systems. 
Ocean voyages being no longer uncommon, I have given rudimental 
principles of navigation in which astronomy is concerned. Few young 
students may ever see the inside of an observatory ; but that is reason 
for their knowing about the instruments there, and prizing opportuni- 
ties to visit such institutions. 

Everywhere has been kept in mind the importance of the student's 
thinking rather than memorizing. Mere memorizing should be ren- 
dered facile ; in treating of the planets, I have therefore presented our 
knowledge of those bodies, not subdivided according to the planets 
themselves as usually, but according to especial elements and features. 
The law of universal gravitation has received fuller exposition than 
commonly in elementary books, its significance demanding this. Bio- 
graphic notes, intrusions in the text, have been relegated to the Index. 

In conclusion, I desire to thank Professor Newcomb of Washington, 
Professor Pickering, Director of Harvard College Observatory, and my 
colleague, Professor Kimball, for helpful suggestions on the proof 
sheets. A few illustrations have been reengraved from the Lehrbuch 
der Kosmischen Physik of Miiller and Peters. P^or many of the excel- 
lent photographs, reader, publisher, and author are indebted to the 
courtesy of astronomers, in particular to M. Tisserand, late Director 
of the Paris Observatory, to the Astronomer Royal, to Professor Pick- 
ering, to Professor Hale ; also to Dr. Isaac Roberts and Professor 
Barnard, both of whose series of astronomical photographs have re- 
ceived the highly honorable award of the gold medal of the Royal 
Astronomical Society. 

DAVID P. TODD. 

Amherst College Observatory. 



CONTENTS 



I. Introductory ...... 

II. The Language of Astronomy . 

III. The Philosophy of the Celestial Sphere 

IV. The Stars in their Courses 

V. The Earth as a Globe .... 

VI. The Earth turns on its Axis . 

VII. The Earth revolves round the Sun 

VIII. The Astronomy of Navigation . 

IX. The Observatory and its Instruments . 

X. The Moon 

XL The Sun ....... 

XII. Eclipses of Sun and Moon 

XIII. The Planets 

XIV. The Argument for Universal Gravitation 
XV. Comets and Meteors 

XVI. The Stars and the Cosmogony 



PAGE 

7 

22 . 

43 

59 

76 

97 

131 

169 

190 

221 

255 
289 

311 
371 
392 
421 



LIST OF COLORED PLATES 

PLATE PAGE 

I. Total Eclipse of the Sun. {¥xo\\\ Hi?/n;iel i/rui Erde, 

edited by Dr. Meyer) ..... Frontispiece 

II. The Sun as revealed by Telescope and Spectro- 

scope. (From Aiuials of Harvard College Observa- 
tory) II- 

III. The North Polar Heavens 60 

IV. The Equatorial Girdle of the Stars ... 62 

V. Solar Prominences. (From Aniials of Harvard College 

Observatory) ......... 283 

VI. ^Three Views of Mars, showing Changing Seasons 

of Hesperia. (^Lowell) 360 

6 ^ 



ASTRONOMY FOR BEGINNERS 



o>«t4o 



^" 



CHAPTER I 



INTRODUCTORY 



ASTRONOMY is the science pertaining to all the 
bodies of the heavens. Parent of the sciences, it is 
the most perfect and beautiful of all. Sir William 
Rowan Hamilton, the eminent mathematician, has called 
astronomy man's golden chain between the earth and the 




I r.e Yerkes Observatory, Professor George E. Hale, Director 

visible heaven, by which we * learn the language and inter- 
pret the oracles of the universe.' This noble science is 
to man a possession both old and ancestral, passing with 
resistless progress from simple shepherds of the Orient 
watching their flocks by night, to the rulers of ancient 

7 



8 Iiit7^odiictory 

empires and the giants of modern thought ; until to-day 
the civiHzed world is dotted with observatories equipped 
with a great variety of instruments for weighing and 
measuring and studying the celestial bodies, each of these 
observatories vying with the other in pure enthusiasm for 
new knowledge of the infinite spaces around us. 

Astronomy a Useful Science. — Many devoted lives have 
been grandly spent in pursuit of this branch of learning ; 
and it would hardly be possible for any one who has given 
even a general glance at their unselfish history to make 
the vulgar inquiry, * What's the use t ' Only a very small 
and unaspiring mind ever asks this question about any 
science which adds to the sum total of our actual knowl- 
edge, least of all with reference to this, — one of the most 
practical of all sciences. Astronomy binds earth and 
heaven in so close a bond that it even maps the one by 
means of the other, and guides fleet and caravan over 
wastes of sea and sand otherwise trackless and impassa- 
ble. By faithful study, even for a short time, it is possible 
to discover many of these uses. They may not at once 
appear to put money into men's pockets or clothes upon 
their backs ; but we have passed the pnxnitive stage of a 
rudely toiling community, where material progress alone is 
the thought and aim. 

Especial Uses. — To specify in part the relations in 
which astronomy is useful: (i) In chronology, — fixing 
many disputed dates of ancient battles, the reigns of kings, 
and other important historic events, and establishing the 
exact length of the units of time requisite for the calendar. 
For example, the surest basis of the chronology of ancient 
Assyria rests upon an eclipse of the sun observed in Nine- 
veh in the middle of the reign of Jeroboam the Second, 
which modern astronortrfeaj calculations prove to have 
taken place on the 15th of Juii-er-B.c^^63. (2) In navi- 



Especial Uses 



gation, — conducting ships from port to port, almost with- 
out risk, thereby saving human Hfe and lessening the 
cost of many of the necessaries of existence. The great 
national observatory^^ at 
Greenwich (page 433) is 
one of those founded for 
the especial and practical 
purpose of improving the 
astronomical means of 
navigation. {^\\). geodesy 
ana in ' surveying, — en- 
abling us to ascertain the 
size of the earth, make 
accurate maps of its con- 
tinents and oceans, and 
run boundaries of coun- 
tries and estates. (4) In 
determining exact time, ' 

— a vast convenience in 
all the affairs of life, par- 
ticularly in the operation 
of railways. In many 
large cities, the dropping 
of a ball on a high tower 
indicates exact noon. 
Every good watch has been carefully rated by an accu- 
rate clock (perhaps in some observatory), which again 
has been corrected by observations of the fixed stars 

— a knowledge of the precise positions of which depends 
upon the faithful patience of a multitude of astronomers 
who have given their lives to this work in the past. 
Indeed, it is hardly an exaggeration to say that there 
is no civilized person in existence whose comfort is not 
enhanced, whose life is not rendered more worth the 




I 



The Time-ball at New York 



lO 



Introductory 



living, or who is not affected, at least indirectly, by the 
work of astronomers, and by those who, though not 
astronomers, are yet practically applying the principles 
of this science to the affairs of everyday life. 

The Sun by Day. — Singularly few persons regard the 
daytime sky. Yet this beautiful and ever-varying spec- 
tacle may be seen 
and enjoyed by all ; 
perhaps that is one 
reason why it is so 
little thought of. 
Even the sordid city 
court, the worst 
tenement district, 
may have its strip 
of blue above, far 
away from noise 
and uncleanliness. 
No buildings are 
high enough to shut 
out this heavenly 
gift entirely. The 
study of the sky in 
daylight, especially 
its clouds, is prop- 
erly part of a sepa- 
rate science, — 
meteorology as dis- 
tinguished from astronomy. The marvelous sun, too, 
by wTiich, as will be seen, we live and m.ov€ and^ have 
our being, is held hardly less a matter of course. 
Here it is that meteorology joins on the boundary of the 
science we take up to-day ; for the sun is one of the chief 
objects of study in modern astronomy, — its distance, its 




Clouds of the Daytime Sky (photographed by Henry) 



'<\ .J Vi '.^ '; '-'Jii' 




Pi,ATO II,— Th^ Sun as R^vkai^ed by Tki^^copk and Spectroscopy. 

{TrouveloL) 



The Sta7^s by Night 



II 




vast size, its apparent motion, the sources of its intense 
light and heat, its constantly changing spots, its constitu- 
tion, the hydrogen prom- 
inences, which seem to 
spring from its edge as 
tongue-like flames, and 
its energies, tirelessly 
radiated into space and 
regnant in all the forms 
of life upon the earth, 
no less than in all those 
phenomena of the at- 
mosphere which we call 
weather. Many of the 
spots on the sun are 
larger than our globe, 
like the one here pic- 
tured. Without fine in- ^" ^"^^^^^ ^""^p°^ ^^^''^^^ 
struments carefully adjusted, the prominences cannot be 
seen except during total eclipses of the sun. ^^^ 
The Stars by Night — But this sense of everyday t'^ 
usualness in great part gives way, once the sun has set, 
and the stars have come forth, as if from their daytime 
hiding. Of course they fill the sky just as truly when 
the world is flooded with sunlight, shining all in their 
appointed places, where the brighter ones may be seen 
with the telescope during the day ; but their feebler light 
is conspicuous only when this greater brilliance is with- 
drawn from our horizon, or when the moon comes in 
between us and the sun, causing a total eclipse. Immanuel 
Kant, a great German philosopher, has said that two things 
filled him with ceaseless awe, — the starry heavens above 
and the moral law within. Even the most prosaic cannot 
but notice and revere the night-time sky, and few are so 



12 



Introduciory 



hopelessly unimaginative as not to be impressed by the 
dark blue dome spangled with its myriad stars. The posi- 
tions of the stars with reference to one another seem to 
remain constant, although they are continually changing . 
their places relatively to objects on the earth. Hence the 
term fixed stars. But this is only seemingly the proper 
expression. In reality, all are speeding through space at 




The Night-time Sky in a Great City 

very. high velocities, but so infinitely removed are the stars 
from us that they appear to be at rest. Although quite 
the reverse, as we now know, from 'fixed,' the term is 
still used, because in the astronomically brief period from 
generation to generation, the changes are so slight that 
the naked eye is powerless to detect them. 

Number of the Brighter Stars. — In ancient times the 
brilliant host of the nightly sky was thought to be 
countless ; but surprising as it may seem, the stars actually 
visible to the unaided eye at a single place in the United 
States do not exceed 2000 or 3000, and only upon ex- 




The Milky Way near the Star 15 Monocerotis, yR = 6 h. 35 m., Decl. N. 10° 
(photographed by Barnard, 1894. Exposure 3k hours) 

13 



14 Introductory 

ceptionally favorable nights may so many be counted 
without a telescope. As an average, on what may be 
termed clear nights, the number thus ordinarily seen at 
any given time is rather less than 2000 ; but this number 
varies greatly with changing conditions of our atmos-" 
phere. If one were to keep count, through the year, of 
all the stars visible to the naked eye in all that part of 
the heavens ever seen from a single place in the United 
States, the total number would be about 4000. 

Number of the Telescopic Stars. — By the use of a small 
telescope, or even an opera glass, the number of visible 
stars is increased enormously. Even in Galileo's time, his 
' optick tube ' revealed an unsuspected and unnumbered 
host, beyond the dreams of any primitive astronomer. 
With our modern telescopes (in which the object glass of 
almost every famous new one has been an advance in size 
upon all its predecessors) the 'blue field of heaven' is 
estimated to contain at least 100,000,000 stars. Beyond 
what is shown even by these telescopes are the remarkable 
revelations of celestial photography, which reproduces 
unerringly upon the sensitive plate uncounted millions of 
other stars too faint for the eye to detect, even when aided 
by the most powerful optical means at our command. 
In a single field embracing but a slight fraction of the 
whole sky, recently charted with the Bruce telescope of 
Harvard Observatory (the largest photographic instrument 
in existence), there were counted no less than 400,000 stars. 
And who can say where this stupendous array ceases 1 

The Constellations. — The names and positions of the 
brighter stars are very easy to remember. By even a cas- 
ual glance at the sky on any clear night, it will be seen 
that the stars make all sorts of figures with one another, — 
squares, triangles, half circles, — and fanciful combinations 
mav be traced in all directions. The ancients called these 



The Yerkcs Telescope 



15 




The Yerkes Telescope of the University of Chicago 



This great telescope was mounted in 1896-97 at Williams Bay, Wisconsin. 
It is the principal instrument of the Yerkes Observatory, and cost about 
^125,000. The glasses for its 40-inch lenses, the largest in the world, were 
made by M, iMantois of Paris, ground and figured by Alvan Clark & Sons 
of Cambridgeport ; and the tube and all the intricate- machinery for han- 
dling the telescope with ease and precision were built by Warner & Svvasey 
of Cleveland. 



i6 



Introductory 



various figures after their gods and heroes, dividing them 
into 48 groups, largely named after the characters asso- 
ciated with the voyage 
of the fabled ship Argo, 
Although these constel- 
lations bear little real 
resemblance to the men, 
animals, and other ob- 
jects named, they too 
are easily learned. Prop- 
erly that is not astron- 
omy, but merely geog- 
raphy of the heavens ; 
yet it is an interesting 
and popular branch of 
knowledge, often lead- 
ing to farther studies 
into the most absorbing 
and uplifting of sciences. 
The Moon. — Of all 
celestial bodies, meteors 
alone excepted, the moon 
is the nearest to us, and 
apparently of about the 
same size as the sun ; 
but this is the result of 
a somewhat curious co- 
incidence, by which the 
sun, although 400 times 
larger than the moon, is 
also very nearly 400 

-:.c ...wv^.. vL^.^OLographed by the Brothers Henry) ,. c ,y 

^ times farther away. 
Even with a small telescope we may generally see the deep 
craters and the rugged mountain peaks of the moon, partly 




M 



The Planets 17 

illuminated by sunlight, while the rest of our satellite is 
turned away from the sun, lying in shadow and seen very 
faintly by the sunlight falling upon it after reflection from 
the earth. Our companion world is dead and cold, its air 
and water almost certainly gone, so that no amount of 
brightest sunshine can of itself bring back any warmth 
of life. Earth and other planets are dark, too, on the 
surface, save for what the sun bestows of brightness and 
warm.th ; but our own planet and some of the others are 
blessed with an encircling atmosphere, best gift after 
sunlight itself, to save and store for our use the sun's heat 
shed lavishly upon us. 

The Planets. — When frequent looking at the nightly 
sky has somewhat familiarized the evening constellations, 
— different at the same hour at the various seasons of 
the year, — one may notice three or four very bright 
stars which do not twinkle. A few evenings' watching 
will show that they are slowly changing their positions 
relatively to other and fainter stars about them. These are 
the planets (^wanderers '), and will at first be thought and 
called stars ; but although speak- 
ing in the most general terms, it 
is proper to refer to them as stars, 
they are worlds, among w^hich 
the earth is one, traveling round 
the sun in nearly circular paths. 
Like our own planet, they receive 
their light from the central orb, 
and reflect it afar. The planets 

and all their moons (called Satel- jupltsr in a Small Telescope 

lites), as well as our moon, give 

light only as reflected sunshine, — second-hand. Some of 
the planets are brighter than most stars, only because 
they are very much nearer to us and to the sun. 
todd's astron. — 2 




i8 



Introductory 



Differences between Stars and Planets. — Besides the 
noticeable change of position of the planets, and their 
shining by reflected light, another difference between 
planets and fixed stars is that, when seen through a tele- 
scope, planets appear larger in size than with the naked 
eye. This the stars never do. Most planets have an 
appreciable breadth, called the disk ; and this seems to 




The Planet Saturn in 1894 (drawn by Barnard with the Lick Telescope) 

grow larger as the power of telescopes is increased. Stars, 
on the contrary, seem to be mere points of light, intensely 
luminous, and infinitely far away. They increase only in 
brilliancy with the size of our largest glasses ; and even 
the strongest lenses cannot produce the slightest effect 
upon the apparent size of these stupendously distant blaz- 
ing suns. Also some of the planets as seen in the tele- 
scope show phases ; in particular, Venus, the brightest 
planet, a familiar glory of the western sky, passing through 
all the changing phases of our moon, — full, quarter, and 
crescent. A planet called Saturn is surrounded by a 
thin ring, as shown in above engraving. It suggested a 
process of evolution called the nebular hypothesis, by 
which stars, planets, and satellites seem to have devel- 
oped into present forms through the operation of natural 
laws. 



The Distances of the Stars 19 

The Fixed Stars are Suns. — All these fixed stars are 
suns like our own — singularly similar, the modern revela- 
tions of the spectroscope tell us, as to material elements 
composing them. Probably, at their inconceivable dis- 
tances from us, these suns afford light and heat to 
uncounted worlds not unlike those in the system of 
planets to which our earth belongs. But if such planets 
exist, they are too near their own central luminaries, and 
too faint for their reflected light ever to reach our far-off 
eyes. One must think of the vaster brilliance of the sun 
as due almost wholly to our relative nearness to him. 
Were the earth to be removed as far from the sun as 
it is distant from the stars, our lord of day would shrink 
to the feeble insignificance of an average star. 

The Distances of the Stars. — The nearest star is so far 
from us that its distance in figures, however expressed, 
remains unapprehended by the human mind. Who can 
conceive of 25 millions of millions of miles .'^ Yet so re- 
mote is our closest stellar neighbor. As the stars v^ry 
enormously in their distances from us, so they are equally 
diverse in their relations to each other. We see them all 
by the light they emit — light which does not come to us in- 
stantaneously, yet with speed almost inconceivably great. 
While one is taking two ordinary steps, at an average 
walking pace, light will travel a distance equal to eight 
times round the world (nearly 200,000 miles). Now, to 
realize in some sense the enormous distance of the nearest 
fixed star from our earth, open a Webster's International 
Dictionary, which contains over 2000 pages of three col- 
umns each, or the equivalent. Begin to read as rapidly as 
you can, and imagine a ray of light to have just left the 
nearest fixed star at the instant you began. By the time 
you have finished a single page, the star's light will have 
sped onward toward the earth no less than 100,000,000 miles. 



20 



Introductory 



Imagine that you could keep right on reading, tirelessly 
and without ceasing, day and night, just as light itself 
travels — how many pages would you have read when the 
ray of light from Alpha Centauri, the nearest fixed star, 
had reached the earth ? You would have read it com- 
pletely through, — not once, or twice, but nearly a hundred 
times. So enormously distant is this nearest of the stars 
that, if it were blotted out of existence this present mo- 
ment, it would continue to shine in its accustomed place 
for more than three years to come. And other stars whose 
distances have been measured are a hundredfold more 
remote. 

The Shooting Stars and Comets. — Very frequent celes- 
tial sights, especially in April, August, and November, are 

the swarms of swiftly-falling 
meteors. They flash across 
the skv and seem to vanish 
into the blackness whence 
they came, burning sparks in 
the starry firmament. On 
rare occasions a fragment of 
a meteor falls down upon the 
surface of the earth, and many 
thousands of such specimens 
are preserved as collections 
of meteorites in various scien- 
tific centers, — Vienna, Lon- 
don, Paris, and Washington. 
Sometimes they are of iron, 
and sometimes of stone. 
Much less common than the 
spectacle of shooting stars 
is that of a majestic comet, whose long and graceful tail 
sweeps many degrees along the sky, sometimes for weeks 




The Great Comet of 1858 



Gravitation - 2 1 

or even months together. All these wandering visitors, 
too, must be studied in their place. 

General Outline. — We know that the stars are suns ; 
that our sun is one of them, seemingly larger only because 
very much nearer ; that he conducts with him through 
space our earth and her companion planets with their 
moons, or satellites; that the stars are all moving through 
the celestial spaces with great velocity, though at such 
enormous distances from us that they appear to be almost 
at rest; that meteors and comets flash into our firmament, 
the former to perish after one bright, sparkling clash with 
our atmosphere, while the latter have their known and 
regular orbits, or paths, some of them coming back within 
our sight at predicted intervals. 

Gravitation. — The mighty power called gravitation holds 
all these whirling, flying, incandescent or white-hot, or 
cold and dead bodies from swerving outside their paths 
in space; and, little by little, the patience and ingenuity 
and genius of man have interpreted many of the laws 
governing them, and have brought to our knowledge 
manifold facts about them, — their weights and distances, 
sizes and motions, and even the elemental substances of 
which they are composed. Their physical appearances, 
as revealed by telescope and camera, will be abundantly 
emphasized. But perhaps the most striking fact in all 
astronomy is that unerring precision with which the 
heavenly bodies move through the celestial spaces in ac- 
cordance with this great law of gravitation, whose action 
enables us to foretell with great accuracy, hundreds of 
years in advance, the places of planets in the starry 
heavens, and the exact hour, minute, and second, when 
eclipses will happen. And progress through the chapters 
of this book will unfold in part the knowledge gained by 
astronomers through centuries of careful investigation. 



CHAPTER II 



THE LANGUAGE OF ASTRONOMY 



NO one can understand even the simplest truths of 
astronomy without first learning the language of pre- 
cision which astronomers use. Only a few terms in 
this language will be necessary at the outset, and they wall 
be illustrated and ideas of them conveyed by means of com- 




How to find True North (Approximately) 

mon objects and simple processes. First, the four cardinal 
points, east, north, west, and south, — terms in constant 
use from the remotest antiquity. 



Plumb-line, Zenith, and Nadir 



23 



How to find the Cardinal Points. ^ Any sharply-pointed object, 
firmly set, may be used as a gnomon for finding the cardinal points. 
But the following method has greater advantages. Place a carefully 
leveled board or table so that the sun may fall freely upon it, from 
about nine o'clock in the morning until three in the afternoon. Fasten 
securely. Near the sunward end of the table, and about eight inches 
above it, fix firmly a card with a smooth pin hole through it. This will 
give a small, oval image of the sun on the table, and its position must 
be marked at nine o'clock, at a quarter past, and at half after nine ; 
again at half after two in the afternoon, a quarter to three, and three 
o'clock. The principle involved is that of the gnomon of Anaximander 
in very compact form. Take especial care that the marked surface, 
whether board or paper, shall not have moved meanwhile. Draw three 
straight lines joining the sun marks, as indicated in the picture oppo- 
site ; connect the nine o'clock mark with the three o'clock one; draw 
a second line connecting the 9:15 mark with that made at 2 : 45 ; and 
a third, joining the 9 : 30 and 2 : 30 marks. These three lines will be 
nearly parallel, and they mark the direction east and west approxi- 
mately, the east end being indicated by the three afternoon marks. 
Three pairs of points are better than one, because clouds may interfere 
with the afternoon observations ; also, we can take the average direc- 
tion of three lines, which will give true east and 
west more accurately than a single line. By the 
simple construction in geometry indicated in the 
illustration, draw a perpendicular to this average 
line ; this perpendicular, then, wdll lie in the direc- 
tion north and south, north lying on the right 
hand as one faces west. Extend these two straight 
lines indefinitely, and they will mark the four car- 
dinal points called east, north, west, and south. 

Plumb-line, Zenith, and Nadir. — Suspend any 
heavy object by a delicate cord attached to a firm 
support, and allow it to come to rest. Draw it to 
one side or the other from its support, and let it 
swing freely. Such an object capable of swinging is 
called a pendulum. The force causing it to swdng 
back and forth is called the attraction of gravity. 
We shall see subsequently that this is the same 
force that makes all bodies fall to the earth ; also 
that it holds the moon, our satellite, in its monthly 
path, or orbit, about us. After swinging back and forth many times, 
the pendulum will come to rest ; and it will do so more quickly if the 
weight or bob of the pendulum is freely suspended in a basin of water. 
A pendulum that has stopped swinging becomes a plumb-line. 




9 



A Plutnb-:ine 



24 The Language of Astronomy 

Imagine the cord of the plumb-line extended both upward to the sky 
and downward through the earth indefinitely. The point overhead 
where the plumb-line intersects the sky is called the zenith ; the oppo- 
site point is called the nadir. 

The Apparent or Visible Horizon. — Looking up to the 
sky, it seems to be arched over us like the inside of a great 
hollow sphere. The dome of the sky is nearly hemispher- 
ical, and seems to most eyes less distant overhead. In 
ordinary inland regions the sky seems to meet the earth 
in an irregular and broken line. This is called the appa- 




Plane of the Sensible Horizon cuts through the Mountains 

rent or visible horizon ; and nearly every point of it, even 
in locations not especially mountainous, will usually be 
considerably above the level of the eye. In cities the 
surrounding buildings, the trees in the park, and the spires 
of churches will lift themselves into our vision, too near by 
to allow any observation of the sky at the exact level of 
the eye. In the country, in Massachusetts, for example, 
it is not always easy, without ascending some great 
height, to reduce the obstacles forming the apparent hori- 
zon to a minimum ; and usually the sensible horizon lies 
far below them all. Objects relatively near, then, whether 



The Sensible Horizon 



25 



houses, grain elevators, churches, forests, or mountains, 
make irregular curves and broken lines which limit the 
outward view in every direction. Their outline marks the 
observer's apparent, or local, or visible horizon. 

The Sensible Horizon. — From the surface of the ocean, or from a 
widely extended plain or prairie, the dome of the sky appears to join 
the earth in a nearly perfect circle about 25 miles in diameter. In Bos- 
ton, for instance, we may take the steamer for Nahant, and for a portion 
of even that short trip our perfect ocean horizon on one side will hardly 

■1 





The Visible Horizon on the Ocean 

be interfered with. In New York a boat trip to Far Rockaway or Long 
Branch will give us a similar opportunity. In Chicago we have a choice 
of ways to get a complete view of the sensible horizon. A car ride 
in almost any direction — to Evanston, perhaps — will show widely 
extended prairies, seeming to stretch to the sky on all sides ; far out 
upon Lake Michigan, the effect upon the observer is like that of the 
ocean; or perchance the Auditorium tower may be ascended, and if the 
distant view is clear, a far-away horizon of the sensible order is within 
sight. Practically in this circle, the four cardinal points are located. 
Imagine a plane passed through these four points. It will pass through 
the eye of the observer, and will essentially be the plane of his sensible 
horizon, neglecting only a small angle called the dip of the horizon, a 



26 The Language of Asironomy 

term used in navigation, and explained in a later chapter. On a small 
piece of cardboard draw two lines at right angles, one of them being 
near the middle of the card. Pierce the card at each end of this line, 
and draw a piece of twine through the holes. Fasten one end of the 
twine to some firm object, and suspend a weight of a few pounds by the 
other end. When the pendulum has come to rest, fasten the bottom 
of the plumb-line carefully in that position, and stretch it taut. Then 
twirl the card round, and the second line on it will point everywhere 
ia the direction of the sensible horizon. 



The sensible horizon, then, is a plane passing through 
the pomt of observation and perpendicular to the plumb- 
line. When the term liorizon alone is used, the sensible 
horizon is meant.. It is a fundamental plane of reference 
in astronomical measurement. 

The Terrestrial Sphere. — A sphere is a solid figure all 
points on whose surface are at the same distance from a 

point within called the 
center. The general 
figure of the earth 
being spherical, it 
/ ^9H^ ^^'"^ ^^ seen that the 

/ ^^^^ directions indicated 

by the terms north, 
south, east, and west, 
if extended in straight 
lines into space, are 
true only for a given 
locality, or position of 
the observer. This is 
because he is situated 
upon the surface of 
a globe or sphere, 

West the same as East at Antipodes i . i j. -l 

and the moment he 
changes his position upon it, his zenith and horizon and 
system of cardinal points all change with him. Down 




Properties of the Celestial Sphere 27 

always means toward the center of this globe ; so that 
if a plumb-line were imagined as extended downward 
through the earth, at the antipodes it would coincide with 
the direction tip. If we go to the opposite side of the 
globe, changing our longitude by 180°, evidently the direc- 
tions called east by us in these two remote localities will 
be exactly opposite to each other in space. So that a con- 
tinuous line, in order to represent a constant direction, 
must have a constant curvature, corresponding to that of 
the surface of the earth. The plane passing through the 
earth's center parallel to the sensible horizon is called the 
rational horizon. 

The Celestial Sphere. — We have spoken about the hemi- 
sphere or dome of the sky. It is obvious from geometry 
that the hemisphere above the sensible horizon must be 
matched by an equal hemisphere inverted, and lying below 
it. This complete and regular form, made by the two 
hemispheres joined, is called the celestial sphere. Sun, 
moon, and all the stars of the firmament are scattered 
apparently at random upon its inner surface. We need 
not now concern ourselves, about the remoteness of the 
bodies in the sky. All appear to be at the same distance 
from us ; and the eye unaided is powerless to find out what 
that distance is. But evidently there may be a very great 
range in their distances, just as there is in the lights of 
different sizes on ships in a harbor, or in the night signals 
along a straight stretch of railway in or near a great city. 
In either case, on a dark night, an inexperienced person 
has little to guide him safely in judging what the distances 
and relative location of the lights may be. 

Properties of the Celestial Sphere. — The celestial sphere, 
notwithstanding its inconceivable magnitude, possesses all 
the properties of a geometric sphere : not only is every 
point of its surface equally distant from a point within 



28 The Language of Astronomy 

called its center (the point where the observer is), but all 
planes cutting the sphere through its center trace out cir- 
cles of equal magnitude upon its surface. These are called 
great circles. All planes cutting the sphere otherwise 
than through its center trace out small circles upon its 
surface. Evidently it is possible to imagine upon any 
sphere as many great circles and as many small circles as 
may be desired. Three systems of circles of the celestial 
sphere, with their related points, lines, and arcs, are in 
common use. They are : 

{A) the Horizon System, 
{B) the Equator System, 
(C) the Ecliptic System. 

{A) The Horizon System. — The great circle that passes 
through the four cardinal points is called, as we have 
seen, the Jiorizon. Upon it is based a system of circles 
of the celestial sphere much used in astronomical de- 
scriptions and measurements. Any great circle traced on 
the celestial sphere by a vertical plane passing through 
the point of observation is called a vei^tical circle. Clearly 
an indefinitely great number of vertical circles may be imag- 
ined as drawn. The planes of all vertical circles intersect 
each other in a vertical line — the plumb-line extended, — 
joining zenith and nadir. Two vertical circles are very 
frequently used, and have especial names : first, the vertical 
circle passing through the north and south points of the 
horizon is the meridian; second, the vertical circle at 
right angles to the plane of the meridian, and passing 
through the east and west points of the horizon, is called 
the prime vertical. Any small circle of the celestial sphere 
cutting it parallel to the horizon is called an ahmicantar. 
Evidently there is no limit to the number of almucantars ; 
one may be imagined as drawn through every star in the 



Change of Horizon System 



29 



sky. The nearer a star is to the zenith, the smaller 
its almucantar, just as parallels of geographic latitude 
upon the earth be- 
come smaller and 
smaller as the poles 
are approached. 
Three hoops of a bar- 
rel tied or tacked to- 
gether, with all the 
angles right angles, 
as in the illustration, 
form an excellent rep- 
resentation of horizon, 
meridian, and prime 
vertical; a much 
smaller hoop (near 
the top) may illustrate 
an almucantar. Such 
a concrete model is a 

necessary aid to many minds in attaining an adequate con- 
ception of the abstract circles of the celestial sphere. 
Essentially they are a pattern of the armillary sphere of 
the ancient astronomy. 

Change of Horizon System with Change of Place. — The 
terms horizon^ meridian^ prime vertical^ and almu- 
cantar are generally applied to the circles upon the 
celestial sphere traced by their planes. The terms are, 
however, often, and properly, employed to designate 
the planes themselves. It will be understood that these 
four terms apply to an observer wherever he may be 
located upon the surface of the earth. If he remains in 
a single position, or has an observatory with a single 
instrument, his horizon plane, meridian, and other circles, 
planes, and points connected with it, have always a con- 




Chief Circles of Horizon System t,J) 



30 



The Language of Astronomy 



stant and definite position, relative to the observer him- 
self. They are imaginary planes and circles which the 
observer carries about with him wherever he goes. The 
moment he changes his locality, by so much even as a 
few feet, he has thereby changed the position of all this 
network, or system of celestial circles, by an amount 
small, to be sure, but readily measurable by the instru- 
ments and methods of the modern astronomer. 

Diurnal Motion and the Diurnal Arc. — The sun, moon, 
and stars, in their everyday motion, appear to cross these 




Co A' 



The Midsummer Sun is Hig^hest and its Diurnal Arc is Longest 



circles in various directions, and at various angles, and 
with various velocities. A few evenings' observation will 
show this. These movements are known as the phe- 
nomena of the diurnal motion. Observe the points where 
the sun rises and sets ; if in the latter half of September 
or March, these will be found to be almost due east and 



Diiirual Motion of a Star Overhead 31 

west. As noon approaches, near which time the sun 
will cross the meridian, his course, in the latitude of the 
United States, will be found to have been, not upward 
along the prime vertical, but obliquely toward the south, 
as illustrated : his paths at various seasons are all in 
parallel planes. He will reach the highest point when 
crossing the meridian, and is then said to adviinate. 
Onward to sunset he describes an arc almost precisely 
symmetrical w^th the forenoon path. This apparent track 
of the sun through the daytime sky, from sunrise to sun- 
set, is called the diitrnil arc ; and either half of it, between 
meridian and horizon, is called the seinidiitrnal arc. Simi- 
larly observe the moon. 

Perhaps it will rise considerably north of east. Watch it as it 
mounts to the meridian. It will cross this pLme only a few degrees 
south of the zenith, and descend the Avestern half of its diurnal arc, 
setting about as far north of true west as it rose north of true east. 
Select very bright stars in other parts of the sky both north and south 
of sun and moon, and observe where they rise and set and culminate. 
It is apparent, then, that the term dhtrnal arc refers only to the interval 
during which a celestial object is above the horizon ; and this inter- 
val of time (for any heavenly body except the sun) may elapse partly 
during actual day and partly during night, or even entirely during the 
night-time. For example, note the rising of some bright star near the 
southeast. How slowly it appears to leave the horizon. Notice its low 
elevation when it reaches the meridian, and its dechning arc in the 
southwest. Evidently its diurnal arc is vecy short ; it has not been 
above the horizon more than seven or eight hours in all. 

The Diurnal Motion of a Star Overhead. — Next select 
a bright star almost overhead. Early in September even- 
ings in the United States, Vega (Alpha Lyra) will be in 
this position. As it descends toward the west, its course 
will seem to curve rapidly toward the north ; and as it 
approaches the northwestern horizon, it will seem to go 
down less and less rapidly, meanwhile moving more and 
more toward the north. Finally, it will disappear only a 



32 The Language of Astro7ioniy 

few degrees west of true north. In making this circuit 
from the meridian to the northern horizon, it will have 
consumed perhaps lo or ii hours; and as there will be 
a similar arc of lO or ii hours between meridian and 
eastern horizon, evidently such a star's diurnal arc may 
be as much as 20 or 22 hours in length. 

The Diurnal Motion of a Circumpolar Star. — Then 
choose a star still farther north, but near the meridian, 
and observe its motion critically. Very noticeable will be 
the fact of its moving away from the meridian less rapidly 
than the star just observed. It will not go nearly so far 
west, and after about six hours it will begin to return 
toward the north. Then, if we could follow it into the 
daylight, six hours later still, or about 12 hours after it 
was first observed, it would be seen nearly due north, and 
at a considerable distance above the horizon. This plane, 
in fact, it will never have reached. It will then continue 
to move backward from west toward east, ascending from 
the horizon at first very slowly, and making an excursion 
as far east of the meridian as it was observed to the west. 
After an interval of 24 hours from the first observation, 
this star will be seen nearly in the first position, just like 
any other star, having described an entire small circle of 
the celestial sphere ; and it would have been visible all the 
time except for the overpowering brilliance of the sun. 

The Pole Star. — If we select a star yet farther north, 
we shall find that it describes an even smaller circle of the 
celestial sphere. This tentative method alone would enable 
us, by a few nights' observations, to select that star which 
describes the smallest circle of all; the bright star known 
as [Stella] Polaris, or the pole star. Next to sun and moon 
the most important object in the heavens, it is always visi- 
ble in all places in the United States when the sky is clear, 
not only by night, but by day with the assistance of a 



Hozv to Find the Pole of tlie Heavens 33 

small telescope. The center of the very small circle which 
Polaris appears to describe every 24 hours is the north 
pole of the heavens. Also the diurnal paths of all other 
stars are central about it. 




Five-hour Trails of Northern Circumpolar Stars (photog-raphed by Barnard) 

How tu find the Pole of the Heavens. — First focus the camera care- 
fully on some very distant object, and mount it in the meridian. Secure 
it firmly, with the lens directed northward and upward at an angle of 
about 45^. As soon as the stars are out, and it has become quite dark, 
take off the cap and leave the plate exposed as long as is convenient, 
or until the beginning of dawn. Development will then show some- 
thing like the above, a series of concentric arcs, the shortest and 
brightest of which will be that of Polaris. Star trails will be broken 
lines, if clouds temporarily intervene. At the center of all these curv- 
ing arcs is the celestial pole itself, always situated in the observer's me- 
ridian ; or strictly speaking, the meridian is the vertical circle passing 
through the pole of the heavens. If the camera is pointed near the celes- 
tial equator, star trails will be straight lines, as on the following page. 
todd's astron. — 3 



34 T^^^ Language of Astronomy 

{B) The Equator System. — The north pole of the 
heavens is a fundamental point of a second system of 
planes and circles of the celestial sphere, just as the zenith 
is the primary point of the horizon system. Imagine 
this horizon system of planes and circles — horizon, prime 
vertical, meridian, and almucantar — to be outlined in a 
connected skeleton upon the vault of the sky. Also think 
of this skeleton system as pivoted at the east and west 




One-hour Trails of Stars in Orion's Belt (photographed by Barnard) 

points, and free to turn about them. Then move the 
zenith point northward along the meridian, until it coin- 
cides with the north pole. The south point of the horizon 
will then have traveled upward along the meridian by an 
angle equal to the distance of the zenith from the north 
pole. Also the north point of the horizon will have been 
depressed below it by an equal arc. In this novel position 
the circles and planes of the celestial sphere need defining 



The Coheres 



35 



anew. What was the zenith is now the north pole of the 
heavens. The horizon has become the celestial equator, 
every point of which is distant 90° from the celestial pole, 
just as the horizon is everywhere 90° from the zenith. What 
were vertical circles now converge toward the poles, the 
southern one of which is depressed below the south horizon 
as much as the northern one is elevated above it. Instead 
of vertical circles they are called, in this position, meridians 
of the celestial sphere, or Jiour circles. They correspond 
to, and are planes extended from, the terrestrial meridians 
of geography. Al- 
mucantars in system 
{A) become parallels 
of declination in sys- 
tem {B), 

The Colures. — Evi- 
dently an hour circle 
may, if desired, be 
drawn through any 
star of the sky. Two 
of these hour circles 
at right angles' to 
each other, have es- 
pecial names ; they 
are counterparts of 
prime vertical and 
meridian in the first 
or horizon system, 
and are called the 
equinoctial cohere and 
the solstitial colure. 

The equator, both the colures, and all the other hour 
circles have nearly constant directions and fixed positions 
among the stars, just as the prime vertical and the merid- 




Chief Circles of Equator System {B) 



36 The Language of Astronorny 

ian have with reference to the landscape at a particular 
place. The absolute position of the north pole, the 
celestial equator, and its colures among the stars can be 
determined at any time ; and the astronomical processes 
by which this is done will be indicated farther on. Equa- 
tor and colures should be concretely illustrated by three 
hoops secured at right angles, as in the horizon system. 

Equator System glides over Horizon System. — It has 
already been seen that the stars themselves, by the diurnal 
motion, cross the planes and circles of the horizon system 
at a great variety of angles and velocities ; evidently then, 
as the circles of the new system are practically fixed 
among the stars, the circles of this equator system must 
be imagined as all the time gliding over and across those 
of the horizon system. Spherical astronomy is a branch 
of the science dealing very largely with the relations of 
equator and horizon systems ; and is mostly concerned 
with the angles that the circles of the horizon system 
make with those of the equator system. The problems 
arising are mostly solved by means of that branch of 
mathematics called spherical trigonometry, which is the 
science of ascertaining all the different parts of triangles 
described on the sphere, from certain parts that have been 
measured by instruments. 

(C) The Ecliptic System. — A third system of planes 
and circles of the celestial sphere, much used in astronomy, 
may best be defined and illustrated here, because it follows 
naturally and readily from the horizon system and the 
equator system. An idea of its relation to these other 
systems is easily obtained on recalling the w^ay in which 
the equator system was derived from the horizon system 
— by pivoting the latter at the east and west points, and 
turning the skeleton horizon system about these pivots, 
until the zenith became the north pole of the heavens. 



Equinoxes and Solstices 



37 



similar way, imagine the equator 
two opposite points where equator 



Now in a precisely 
system pivoted at the 
and meridian cross. 
Then carry the north 
pole toward the west 
23J°. The equator 
will then have as- 
sumed a position in- 
clined by an angle of 
23^° to its former 
position. It will, in 
short, have become 
the ecliptic ; and in 
this novel relation 
nearly all the ele- 
ments of the celestial 
sphere must again 
be defined. A third 
system of hoops 
should be arranged 
as in the illustration. 
The ecliptic, as we 
shall see farther on, 
is the path in which 

the sun seems to travel completely round the sky once 
every year — a motion entirely distinct from that now 
under consideration. 

Parallels of Latitude, Equinoxes and Solstices. — What 
was the north pole of the heavens becomes, in the ecliptic 
system, the north ecliptic pole. The equator itself, as 
has been said, is now the ecliptic. What were vertical 
circles in the horizon system, and hour circles in the 
equator system, are now ecliptic meridians. As almucan- 
tars became parallels of declination, so now parallels of 




Chief Circles of Ecliptic System \C) 



38 The Language of Astronomy 

declination become parallels of celestial latitude. Upper 
of the two pivotal points upon which equator turned 
about meridian is called the Vernal Equinox^ or First of 
Aries; its opposite point, i?>o° ?iWdiy, tht Aicttimnal Equi- 
nox. Or the equinoxes are, simply, two opposite points of 
the celestial sphere where equator and ecliptic cross each 
other. The word equinox signifies equality of day and 
night ; and these points have this name because when the 
sun is exactly at either of them (in spring and autumn), 
it rises due east and sets due west. As the relations in 
the figure opposite show, it is 12 hours above the horizon, 
making the day, and an equal interval of 12 hours be- 
low the horizon. Day and night are therefore equal in 
duration. Passing along the ecliptic eastward 90° from 
the vernal equinox, a point is reached that bears the 
name Sinnnier Solstice {\ht sun's place in the latter part of 
June). Exactly opposite to it in the sky, or 90° beyond 
the autumnal equinox, is situated the Winter Solstice (the 
position of the sun just before Christmas). 

Ecliptic System glides over Horizon System. — The eclip- 
tic system of planes and circles maintains an almost in- 
variable relation to the equator system and to the fixed 
stars. Therefore it also must glide over the seemingly 
stationary circles of the horizon system, in much the same 
manner that the planes and circles of the equator system do. 
In consequence, however, of the angle of 23^-° between 
equator and ecliptic the constantly varying relations of 
the ecliptic system to the horizon system will be more 
intricate than those of the equator system to the horizon 
system. But all these relations are readily understood, 
and may be completely solved by the processes of spheri- 
cal astronomy. 

The relation of equator to ecliptic, and their apparent daily motion 
through the sky, may be well illustrated by a plain model like the one 



Ecliptic System over Horizon System 39 



here shown — two pasteboard disks cut together and secured to an 
ordinary thread-spool sHpped on a lead pencil pointing upward to the 
pole, and twirled round in the direction of the arrows.. In the first 
place, the north pole of the ecliptic, being 23P from the north pole 
of the heavens, is always distant 66} from the equator, and so seems 
to move round the pole once every day, exactly as if it were a star in 
that position. Everywhere in the United States the north ecliptic pole 




Model showing Apparent- Motion of Equator and Ecliptic 

is perpetually above the horizon. The solstices, being points 23 J° from 
the equator, the summer solstice north of it, and the winter solstice 
south, they also seem to move round the sky obliquely to the vertical 
circles of the horizon system. As the axis of revolution of the celestial 
sphere passes through the north and south poles of the equator system, 
the equator revolves round in its own plane, like a pulley on a shaft, and 
is always parallel to itself. Evidently, then, the ecliptic must partake 
of a wobbling motion because of its constant inclination of 23J'' to that 
seemingly stationary circle among the stars, the celestial equator. These 
three systems of circles — (^) the horizon system^ {[]) the equator system^ 
(C) the ecliptic system — comprise all that are in general use by the 
astronomers of the present day. 



40 



The Language of Astronomy 



Usual Astronomical Symbols. — There is a variety of 
symbols in common use for expressing in abbreviated form 
the names of sun, moon, and planets, their location in the 
sky, the signs of the zodiac, and so on. Some of them are 
frequently employed in other sciences with differing signi- 
fications, but their astronomical meanings are as follows : — 



= the sun. 

([; = the moon. 

# = the new moon. 

O = the full moon. 

(^ = conjunction, or the same in 1 

D = quadrature, or differing 90° in \ 

§ — opposition, or differing 180^ in j 

S^ = the ascending node. 



either longitude or 
rio^ht ascension. 



IJ = Mercury. 
9 = Venus. 
© == the earth. 
Z = Mars. 
^ = Jupiter. 
\l — Saturn. 
g = Uranus. 
t|; = Neptune. 



And for the signs of the zodiac (not the constellations of the same 
name), the following: — 



(I) 


T Aries 


(II) 


H Taurus 


(III) 


n Gemini 


(IV) 


55 Cancer 


(V) 


SI Leo 


(VI) 


n^ Virgo 



Spring 
sio^ns. 



Summer 
sio^ns. 



(VII) 
(VIII) 

(I.X) 

(X) 

(XI) 

(XII) 



:^ Libra 
TTL Scorpio 
/ Sagittarius 

V^ Capricornus 
ZiZ Aquarius 
X Pisces 



Autumn 
sio:ns. 



Winter 

sio^ns. 



The explanation of technical terms used above will be given subse- 
quently in appropriate paragraphs. 

Expressing Large Numbers. — In astronomy there is frequent oc- 
casion to express very large numbers, because our earth is so small a 
part of the universe that terrestrial units often have to be multiplied 
over and over again, in order to represent celestial magnitudes. In 
this book, and in accordance with American usage generally, the 
French system of enumeration is used. From one million upward, it 
is as follows : — 

1,000,000 = one million 
1,000,000,000 = one billion The usual 

1,000,000,000.000 = one trillion 1^ or 

1,000,000,000,000,000 = one quadrillion French system. 
etc. etc. 

through quintillions, sextillions, and so on ; the Latin terms being 
employed, and each order being 1000 times that next preceding it. It 



Directions in the Heavens 41 

is necessary, however, to note that in works on astronomy published in 
England, and now widely circulated in America, the English system of 
enumeration is always employed. The terms billion, triUion, quadrillion, 
and so on are used, but with entirely different signification : each is one 
million, instead of 1000, times the one next preceding it. So that 

1,000,000 = one million (English) 

= one million (French) 

1,000,000,000,000 = one billion (English) 

= one trillion (French) 

1,000,000,000,000,000,000 = one trillion (English) 

— one quintillion (French) 
Also, very large numbers are often expressed by an abridged or 
algebraic notation, in which there is no ambiguity. 

Thus, 3 X lo^ = 3,000,000,000 = three billions (French) 
6 X lo^"^ = 6,000,000,000,000 = six billions (English) 

= six trillions (French) 
The small figure above the 10 is called an exponent, and indicates 
the number of times that 10 is taken as a multiplier. 

East and West, North and South, in the Heavens. — 

Ordinary and restricted use of these terms, as adopted 
from geography, has already been defined: north and south 
state the direction of the true meridian ; an east and west 
line is horizontal and at right angles to a north and south 
one. This use of these terms is wholly confined to the 
planes and circles of system (^4), whose fundamental plane 
is the horizon. When, however, we pass to systems (j5) 
and {C\ the meaning of the terms east and west, 7iorth and 
souths changes also, to correspond with their fundamental 
planes. As related to these systems, then, we must define 
north, south, east, and west anew. North is the direction 
from any celestial body toward the north pole of the 
heavens ; it is a constantly curving direction along the 
hour circle passing through that body. Similarly, south 
is the opposite direction, along the same hour circle, 
toward the south pole. Immediately underneath the 
pole, south, in system {B\ means toward the north point 



42 The Language of Astronomy 

of the horizon. East and west lie along equator and 
parallels of declination, in curving directions on the celes- 
tial sphere. When facing toward the south, east is the 
direction toward the left, or counter-clockwise around 
equator and parallels. The farther north or south ' a 
star is, the smaller its parallel, and the more rapid the 
curvature of the direction east and west from it. Also 
the terms east and west, nortJi and south, are often used 
with reference to the planes and circles of system (C); 
north and south then lie along ecliptic meridians, and 
east and west are at right angles to these meridians, in 
the curving direction of ecliptic and parallels of celestial 
latitude. East is counter-clockwise, as in system {B\ and 
north is toward the north pole of the ecliptic. 

We are now prepared to consider the relations of these 
three systems to the work of the practical astronomer, to 
study the terminology of each, and to trace their points of 
geometric likeness philosophically. 



CHAPTER III 



THE PHILOSOPHY OF THE CELESTIAL SPHERE 



AS the conception of the celestial sphere is now under- 
stood, we next give the reasons underlying the differ- 
ent systems already explained. These reasons are 
fundamental, having their origin in the principles of geome- 
try itself. They have been known and accepted since the 
days of Euclid (b.c. 280), who first gave a rational explana- 
tion of all those ordinary phenomena of the celestial sphere 
that the ancients s °o 

were able to ob- 
serve. Practical 
astronomy is the 
science of accurate 
observation and 
calculation of the 
positions of the 
heavenly bodies. 
In order that it 
should advance 
from a rudimen- 
tary beginning, the 
observations, as 
well as the mathe- 
matical processes by which they were calculated, had 
to be accurate. Precise observation was possible only 
when the heavenly bodies could be referred to some 
established point, or circle, or plane. Naturally the 




All Circles are divided into 360 Degrees 



43 



44 Philosophy of the Celestial Sphere 

horizon was the first plane of reference, because the 
rising and setting of sun and moon and the brighter stars 
could be watched quite definitely. This fact explains the 
origin of the fundamental plane of the horizon system. 
Its related points, circles, and planes came naturally and 
necessarily from the principles of geometry. 

The Measure of Angles. — In astronomical measure- 
ments, circles of all possible sizes are dealt with ; and 
every circle regardless of its size is divided into 360°. 
The degree is a unit of angular measure, not of length ; 
and its value as described on a circular arc varies uniformly 
with the size of the circle. In concentric circles, for ex- 
ample, the number of degrees included between any two 
radii, as illustrated on the preceding page, is the same 
in all circles. Every degree is divided into 60^, and every 
minute into 6d^ . Do not confuse with the same symbols, 
often used to designate feet and inches. 

Light moves in Straight Lines. — All astronomy is based 
on the truth of the proposition that, in a homogeneous 
medium like the ether, a weightless substance filling space, 
light moves in straight lines. The physicist demonstrates 
this from the wave theory of the motion of light. 

The nature of a homogeneous medium may be illustrated by contrast 
with one that is not so. Look out of the window at objects seen just 
above the top of a heated radiator. They appear to be quivering and 
indistinct. We know that such objects — buildings, signs, trees — are 
really not distorted, as they seem to be ; and we refer this temporary 
appearance to its true cause — the irregular expansion of the air sur- 
rounding the radiator. A portion of the medium, then, through which 
the light has passed, from the objects outside to the eye, is not homo- 
geneous ; and we know that if the radiator and the air round it were 
of the same temperature, there would be no such blending and scattering 
of the rays. The light passing over a heated chimney, the air above an 
asphalt walk on which the sun is shining, a flagstaff seemingly cut in 
two on a sunny day (when the eye is placed close to it and directed 
upward), — these and many other simple phenomena have a like origin. 
That violent twinkling of the stars which adds so much to the beauty 



Angles and Distances 



45 



of a winter night is due in large part to a vigorous commingling of 
warm air with cold, causing departure of the light-bearing medium from 
a perfectly homogeneous structure. On such nights the telescope 
cannot greatly assist the eye in astronomical observations. 

Angles and Distances. — As light moves in straight Hnes, 
the angle which a body seems to fill, or subtend, is wholly 
dependent upon its distance from the eve. The more remote 




The Nearer the Track, the Broader it seems (Instantaneous Photograph by Trowbridge ) 

a given object is, the smaller the angle it subtends, and the 
nearer it is, the greater this angle. We do not always think 
of this when crossing a straight stretch of railw^ay track, 
although we know that the rails are everywhere the same 
distance apart. But the camera, by projecting all objects 
on a plane surface regardless of their distance, brings out 
prominently the great difference in the angular breadth 
of the track near by and far away, so well shown in the 
picture. By trial we readily verify the following law : — 



46 



Philosophy of the Celestial Sphere 



Aiigles sitb tended by a given object are inversely prop oi'tional 
to the distances at which it is placed. Consequently a 
number of bodies of various sizes — the silver dollar, the 
saucer, and the bicycle wheel, as shown in the illustra- 
tion — may all subtend exactly the same angle, provided 
they are placed at suitable distances. Obviously, then, it 
is verv indefinite to say that the moon looks as big as a 




If Bodies fill the Same Angle, their Size is Proportional to their Distance 

dinner plate or a cart wheel, or anything else, unless at the 
same time it is stated how far from the eye the dinner 
plate or cart wheel or other object is supposed to be. 

Moon and the Radian are Standards. — Observation 
shows that the moon actually subtends an angle of about 
one half a degree ; and it has been demonstrated by geom- 
etry that a sphere whose distance is 



206,000 1 

3,400 \ times its diameter just fills an angle of 

57 J 



These numbers are obtained accurately as follows : Recalling the 
rule of mensuration concerning the circle, whose radius is r, its circum- 
ference, or 360° = 2 7rr, TT being the familiar 3.14159, or 3i. But as 

2 7rr = 360° = 21,600' — 1,296,000", 

^ = 57r= 3.438'= 206.265". 

The angle r is a convenient unit of angular measure. As it is the 
arc measured on the circumference of any circle by bending the radius 
round it, this angle is often called the radian. 



Altitude and Azimuth 



47 



So that if the distance of an object from the eye is 
equal to 115 times its diameter, it will subtend the same 
angle that the moon does, and so will appear to be of 
the same size as the moon. The eye is often deceived in 
the distance and size of objects, generally placing them 
much nearer than they should be. This experiment is 
very easily tried : an ordinary copper cent, in order to 
fill the same angle as the moon should be placed at a 
distance of about seven feet ; while a silver dollar should 
be nearly 14^ feet aw^ay. The moon, then, alw^ays filling 
nearly the same angle of ^^-°, is an excellent standard of 
angular value ; a small unit of arc measure. To express 
the apparent distance of a planet, for example, from a star 
alongside it, estimate how many times the moon's disk 
could be contained between the two objects; then half 
this number will express the distance roughly in degrees. 
Though the result may be somewhat erroneous, the prin- 
ciple is correct. 

Altitude and Azimuth. — Altitude is the angular dis- 
tance of a body above the horizon ; and it is measured 





Stars of Equal Altitude 



Stars of Equal Azimuth 



along the arc of the vertical circle passing through the 
body. Evidently the altitude of the zenith is 90°, and 
this is the maximum altitude possible. Oftentimes the 



48 Philosophy of the Celestial Sphere 

term ze^iitli distajzce is used ; it is always equal to the 
difference between 90° and the altitude. But in order to 
fix the position of a body in the sky, it is not sufficient 
to give its altitude alone. That simply tells us that it 
is to be found somewhere in a particular small circle, or 
almucantar ; but as it may be anywhere in that circle, a 
second element, called azirniitli, becomes necessary. This 
tells us in what part of the almucantar the star is to be 
found. Azimuth is the angular distance of a body from 
the meridian ; and it is measured along the horizon from 
the south point clockwise ( that is, in the direction of mo- 
tion of the hands of a clock), or through the points west, 
north, east, to the foot of the star's vertical circle. Azi- 
muth, then, may evidently be as great as 360^. The position 
of a star in the northwest, and 40° from the zenith, would 
be recorded as follows: altitude 50°, azimuth 135°. One 
at 10° from the zenith, but in the southeast, would be: 
altitude 80°, azimuth 315°. The figures (page 47) make 
it clear that many stars may have equal altitudes, although 
their azimuths all differ ; while yet others, if located on 
the same vertical circle, may have equal azimuths, although 
their altitudes range between o^ and 90°. 

A Simple Altazimuth Instrument. — This simple and readily built 
instrument is all that is needed to find altitudes and azimuths. Of 
course the measures will be made roughly, but the principles are per- 
fectly correct. The illustration shows plainly the essentials of construc- 
tion. From the corners of a firm board base about two feet square, let 
four braces converge, to hold an upright bearing, just below the azimuth 
circle. Through this bearing run an upright pole or straight piece of 
gas pipe, letting it rest in a socket on the base, in which it is free to 
turn round. A broom handle run through two holes bored in the mid- 
dle of two opposite sides of a packing box will do very well, in default 
of anything better. Just above the azimuth circle attach to the upright 
axis a collar with a pointer equal in length to the radius of the azimuth 
circle. It is more convenient if this collar is fastened by a set screw. 
The circle is made of board, to which is glued a circle of paper or 



Use of the Altazimuth 



49 



thin card, divided in degrees, beginning witli o'^ at S, and running 
through 90° at W, 180° at N, 270'^ at E, and so on. After dividing- 
and numbering, tlie circle may be covered witli two or three coats of 
thin shellac, in order to preserve 
it. Attach to the top of the 
vertical axis a second circle, the 
altitude circle, divided through 
its upper half, from 0° on each 
side up to 90°, or the zenith. 
Through the center of the altitude 
circle run a horizontal bearing ; 
it is better if large, say \ inch or 
more, because the index arm 
attached to it will then turn more 
evenly, and stop at any required 
position more sharply. In line 
with the index point and the cen- 
ter of the bearing, attach two 
sights near the ends of the arm. 
Essentially the altazimuth instru- 
ment is then complete. Sights 
for use upon stars with the naked 
eye should be of about this size 

and construction : 

The aperture of 
Model Sight about 1 inch does 
not diminish the star's light, and 
the small cross threads or wires 
give the means of fairly accurate 
observation. 

Use of the Altazimuth. — To 
use it, level the azimuth circle, 
and bring the line through N 
and S to coincide with the merid- 
ian, already found. See that the 
line of zeros of the altitude circle 
is, as nearly as may be, at right 
angles to the vertical axis. 
Point the sights in the Hne of 

the meridian, and while looking northward, clamp the azimuth pointer 
exactly at 180°, by means of its collar. The instrument is then ready 
for use ; and on pointing it at any celestial body, its altitude and 
azimuth at the time of observation may be read directly at the ends of 
the pointers of the two circles. If the instrument has been made and 
todd's astron. — 4 




Model of the Altazimuth 



50 Philosophy of the Celestial Sphere 

adjusted with even moderate care, its readings will pretty surely be 
within one degree of the truth ; and for practicing the eye in roughly 
estimating altitudes and azimuths at a glance, nothing could be better. 
Also take the altitude of the sun and stars when on the meridian and 
the prime vertical. To observe the sun most conveniently, let its rays 
pass through a pin hole at the upper end of the index, or pointer," and 
fall upon a card at the lower end with a cross marked upon it ; care 
being taken that the line of the pin hole and the cross is parallel to the 
line of sio:hts. 



Origin of the Equator System. — The motion of the 
celestial sphere is continually changing the altitude and 
azimuth of a star. Consequently the horizon and its con- 
nected circles are a very inconvenient system of noting the 
positions of stars with reference to each other ; even the 
ancients had observed that these bodies did not seem to 
move at all among themselves from age to age. It was 
natural and necessary therefore to devise a system of co- 
ordinates, as it is called, in which the stars should have 
their positions fixed, or nearly so. From the time of 
Euclid, at least, a philosopher here and there was satisfied 
that the earth is round, that it turns on its axis, and that 
the axis points in a nearly constant direction among the 
stars. Readily enough, then, arose the second, or equator 
system of elements of the celestial sphere ; the upper end 
of the earth's axis prolonged to the stars gave the primal 
point of the system — the north pole of the heavens. 
Everywhere 90° from it is the great circle girdling the sky, 
in the plane of the earth's equator extended, and called 
therefrom the celestial equator. 

Declination. — This plane or circle (often termed the equi- 
noctial, but generally called the equator simply), becomes 
the fundamental reference plane of the equator system 
{B\ It sustains exactly the relation to the equator system 
that the horizon has to the horizon system {^A). And, 
similarly, two terms are necessary to fix the position of a 



Right Ascension 51 

star relatively to the equator. First, the declination, which 
is the counterpart of altitude in system (^A). The declina- 
tion of a body is its angular distance from the equator ; and 
it is measured north or south from that plane, along the 
hour circle passing through the body. If the star is north 
of the equator, it is said to be in nortli or plus declination; 
if south, then in minus or soutli declination. Evidently, 
stars north of the equator may have any possible declina- 
tion up to plus 90°, the position of the north pole ; and stars 
south of the equator cannot exceed a declination of minus 
90°. The symbol for declination is decl, or simply h (the 
small Greek letter delta). Sometimes the term north polar 
distance is substituted for declination ; and it is counted 
along the star's hour circle southward, from the north pole, 
right through the equator if necessary. North polar dis- 
tance cannot exceed 180°, the position of the south pole of 
the heavens. For example, the north polar distance of a 
star in declination +20° is 70°; and if the declination is 
— 22°, the north polar distance is 112°. 

Right Ascension. — Recalling again the terms and circles 
of the horizon system, it is apparent that declination 
alone cannot fix a star's position on the celestial sphere 
any more than mere altitude can. It would be like try- 
ing to tell exactly where a place on the earth is by giving its 
latitude only; the longitude, or angular distance on the 
earth's equator from a prime meridian must be given also. 
So the companion term for declination is right ascension ; 
and it is the counterpart of azimuth in the horizon sys- 
tem {A). But note two points of difference. The right 
ascension of a body is its angular distance from the vernal 
equinox (a point in the equator whose definition has already 
been given on page 38). Right ascension is measured 
eastward, or counter-clockwise, along the equator, to the 
hour circle, passing through the body. It may be meas- 



52 



Philosophy of the Celestial Sphere 



ured all the way round the heavens, and therefore may 
be as great as 360"^. But as a matter of convenience 
purely, right ascension is generally denoted in hours, not 
degrees (figure on page 39). As 24 hours comprise the 
entire round of the sky, and 360° do the same, one may be 
substituted for the other. Each hour, then, will comprise 
as many degrees as 24 is contained times in 360; that 




Stars of Equal Declination 



Stars of Equal Right Ascension 



is, 15. Also hours are divided into minutes and minutes 
sub-divided into seconds of time, just as degrees are, into 
minutes and seconds of arc. So that we have : — 



I h. = i: 



I m. 

I s. 



15 
15' 



and 



I i" = 0.0667 s. 



These are relations constantly required in astronomy. 
Usual symbols for right ascension are r. a., or ^r, or 
simply a (the small Greek letter alplia), standing for 
ascensio recta. The figures make it clear that stars may 
have equal right ascension, although their declinations 
differ widely, and vice versa. 

The Equatorial Telescope. — Just as the altazimuth is 
an instrument whose motions correspond to the horizon 
system, so the motions of the equatorial telescope corre- 
spond to the equator system. This instrument, generally 



Tlie Egitatorial Telescope 



53 



called merely the equatorial, is a form of mounting which 
enables a star to be followed in its diurnal motion by turn- 
ing the telescope on only one axis. 

This axis is ahvays parallel to the axis of the earth, and is called the 
i):)lar axis. As it must point toward the north pole of the heavens, the 
polar axis will 
stand at about 
the angle shown 
in the picture. 
for all places in 
the United 
States. The 
simplest way to 
understand an 
equatorial is to 
regard it as an 
altazimuth with 
its principal or 
vertical axis 
tilted northward 
until it points 
to the pole 
The azimuth cir- 
cle then becomes 
the hoii7' circle of 
the equatorial : 
the horizontal 
axis becomes the 
declination aXiS 
of the equato- 
rial ; and the 
circle attached 
to it is called the 
declination circle 
(the counterpart 
of the altitude 
circle in the 

altazim.Lith). At one end of the declination axis and at right angles to 
it the telescope tube is attached, as shown. The model in the illustra- 
tion may be constructed by any clever boy. The axes are pine rods 
running through wooden bearings, and it is well to soak them with hot 
paraffin. The telescope tube is a large pasteboard roll. 




Model of the Equatorial Telescope 



54 



Philosophy of the Celestial Sphere 



How to adjust and use this Equatorial. — Having already found 
direction of the meridian, the polar axis must be brought into its plane, 
and the north end of this axis elevated to an angle equal to the latitude. 
This can be taken accurately enough from any map of the United States. 

Draw a line on the out- 
side of the bearing of 
the polar axis parallel 
to the axis itself; and 
across this line, at an 
angle equal to the lati- 
tude (laid off with a 
protractor), draw an- 
other line which will be 
nearly horizontal. The 
adjustment is completed 
by means of an ordi- 
nary artisan's level, 
placed alongside this 
second line. Take out 
the object glass and eye- 
piece, and point the tele- 
scope at the zenith, as 
nearly as the eye can 
judge. Then hang a 
plumb-line through the 
tube, suspending it from 
the center of the upper 
end, and continuing to 
adjust the tube till the 
line hangs centrally 
through it. While the 
tube remains fixed in 
this position, set the 
hour circle to read zero, 
and the declination circle 
to a number of degrees 
equal to the latitude. 
The model equatorial is 
then readv to use. Dec- 




1 0-Inch Equatorial (Warner & S'/vasey 



linations can be read from the declination circle directly, bringing 
any heavenly body into the center of the field of view. And right 
ascensions can be found when the hour angle of the vernal equinox 
is known. A method of finding this will be given in the next chapter 
(p. 66). Distinguish between the double and differing significations 



Celestial Latitjidc 55 

of the term hour circle : when the equatorial is adjusted, I'ls hour circle, 
being parallel to the terrestrial equator, is therefore at right angles to 
f/ic hour circles of the celestial sphere. 

Telescopes as mounted in Observatories. — Nearly all the telescopes 
in observatories are mounted equatorially. The cardinal principles 
of these mountings are similar to those of the model already given. 
An equatorial telescope is shown in the illustration opposite. The 
small tube at the lower end of the large one and parallel to it is a 
short telescope called the ' finder,' because it has a large field of view, 
and is used as a convenience in finding objects and bringing the large 
telescope to bear upon them. Iron piers, nearly cylindrical in the best 
mountings, but often rectangular, are now generally employed in sup- 
porting the axes of telescopes. An hour circle is sometimes attached 
to the upper end of the polar axis, as shown ; and geared to the out- 
side of this circle is a screw or worm, turned by clockw^ork (underneath 
in the middle of the pier) . The clock is so regulated as to turn the 
polar axis once completely round from east toward west in the same 
period that the earth turns once completely round on its axis from 
west toward east. When a star has been placed in the field of view, 
and the axis clamped, the clock maintains it there without readjusting, 
as long as the observer may care to watch. Each axis of a large 
equatorial is provided with a mechanical convenience called a ^ slow 
motion,' one for right ascension and one for declination. These 
devices are operated by handles (at the right of the tube), which can 
be turned by the observer while looking through the eyepiece ; and 
they enable him to move an object slow^ly from one part of the field 
of view to another, as required. 



Celestial Latitude. — The third system of coordinates of 
the celestial sphere — (C) the ecliptic system — is founded 
on the path which the sun seems to travel among the stars, 
going once around the entire heavens every year. In fact, 
the ecliptic is usually defined as the apparent annual path 
of the sun's center. This path is a great circle of the 
celestial sphere. And as it always remains constant in 
position, relatively to the fixed stars, its convenience as a 
fundamental plane of reference is easy to see. The name 
ecliptic is applied, because eclipses of sun and moon are 
possible only when our satellite is in or near this path. 
Upon the ecliptic as a fundamental plane is based a sys- 



56 Philosophy of the Celestial Sphere 

tern of coordinates, precisely as in the equator system (^). 
Celestial latitude, or a star's latitude merely, is its angular 
distance from the ecliptic ; and it is measured north or 
south from that plane, along the ecliptic meridian passing 
through the star. Latitude is the counterpart of altitude 
in the horizon system, and of declination in the equator 
system. If the star is north of the ecliptic, it is said to 
be in 7iorth ox plus latitude; if south, then in miniLS or south 
latitude. No star can exceed ± 90° in latitude. As the 
center of the sun travels almost exactly along the ecliptic, 
year in and year out, its latitude is always practically zero. 
The symbol for latitude is /3 (the small Greek letter beta). 
Sometimes the term ecliptic north polar distance is conven- 
ient ; it is measured southward along the ecliptic meridian 
passing through the star. It is independent of the ecliptic 
itself, and may have any value from 0° to 180°, according 
to the star's place in the heavens. A star whose latitude 
is — 38° is located in ecliptic north polar distance 128°. 

Celestial Longitude. — Celestial longitude is the term 
used to designate the angular distance of a star from the 
vernal equinox, measured eastward along the ecliptic to 
that ecliptic meridian which passes through the star. It 
is counted in degrees from 0° all the way round the 
heavens to 360° if necessary. By drawing a figure simi- 
lar to that on page 52, and replacing the celestial pole 
by the pole of the ecliptic, it becomes clear that all stars 
on any parallel of latitude have the same latitude, no 
matter what their longitudes^ may be ; and that all stars 
on any half meridian of longitude included between the 
ecliptic poles must have the same longitude, although their 
latitudes may differ widely. As the equinoxes mark the 
intersection of equator and ecliptic, they must both be in 
equator and ecliptic alike. On the ecliptic, and midway 
between the two equinoxes, are two points, called the 



Summary and Correlation of Terms 57 

solstices. Hence the name of the hour circle, or cohire 
which passes through them — the solstitial colure. At the 
times of the solstices, the sun's declination remains for a 
few days very nearly its maximum, or 23-^°. It was this 
apparent standing still of the sun with reference to the 
equator (north of the equator in summer, and south of it 
in winter) which gave rise to the name solstice. 



In observing the positions of the lieavenly bodies before the inven- 
tion of clocks, the ancient astronomers, particularly Tycho Brahe, used 
a type of astronomical instru- 



ment called the ecliptic astro- 
labe^ a kind of armillary sphere, 
in which the longitude and 
latitude of a star could be read 
at once from the circles. But 
instruments of this character 
are now entirely out of date, 
only a few being preserved in 
astronomical museums, the 
principal one of which is at 
the Paris Observatory. The 
astronomers of to-day never 
determine the longitude and 
latitude of a body by direct 
observation, but always by 
mathematical calculation from 
the right ascension and decli- 
nation ; because the longitude 
and latitude can be obtained in 
this way with the highest accu- 
racy. 




The Ecliptic Astrolabe 



Summary and Correlation of Terms. — Correlation of the 
three systems just described, and of the terms used in con- 
nection with each, is now in order. In the first column is 
the nomenclature of system (/i), with the horizon for the 
reference plane; in the second column, the terminology of 
system {B\ in which the celestial equator is the funda- 



58 



Philosophy of the Celestial Sphere 



mental plane ; and in the third column are found the 
corresponding points, planes, and elements referred to 
the ecliptic system (C): — 

The Philosophy of the Celestial Sphere 



In the Horizon System (/i) 



Becomes in the Equator 
System {B) 



Becomes in the Ecliptic 
System (C) 



Horizon 


Celestial equator 


Ecliptic 


Vertical circle 


Hour circle 


Ecliotic meridian 


Zenith 


North pole 


N. pole of the ecliptic 


Meridian 


Equinoctial colure 


Ecliptic meridian 


Prime vertical 


Solstitial colure 


Solstitial colure 


Azimuth {iiegative) 


Right ascension 


Celestial longitude 


Altitude 


DecHnation (N.) 


Celestial latitude (N.) 



These three systems of planes and circles of the celes- 
tial sphere comprise all those used by astronomers, ex- 
cept in the very advanced investigations of mathematical 
and stellar astronomy. 



CHAPTER IV 

THE STARS IN THEIR COURSES 

THE fundamental framework for our knowledge of the 
heavens may now be regarded as complete. We 
next consider its relations from different points of 
view on earth, at first filling in details of the stars as. neces- 
sary points of reference in the sky. 

The Constellations. — In a very early age of the world, 
the surface of the celestial sphere was imagined to be cov- 
ered by figures, human and other, connecting different 
stars and groups of stars together in a fashion sometimes 
clear, though usually grotesque. The groups of stars 
making up these imaginary figures in different parts of 
the sky are called constellations. Eudoxus (b.c. 370) bor- 
rowed from Egyptian astronomers the conception of the 
celestial sphere, bringing it to Greece, and first outlining 
upon it the ecliptic and equator with the more prominent 
constellations. About 60 are well recognized, although the 
whole number is nearly twice as great. This ancient, and 
in most respects inconvenient, method of naming and 
designating the stars is retained to the present day. In 
general, small letters of the Greek alphabet are used to 
indicate the more prominent stars of a constellation, a 
representing its brightest star, /3 the next, 7 the third, 
and so on. The Greek letter is followed by the Latin 
genitive of name of constellation ; thus a Orionis is the 
most conspicuous star in the constellation of Orion, 7 Vir- 
ginis is the third star in order of brightness in Virgo, and 

59 



6o The Stars in their Courses 

so on. Following are these letters, written either as sym- 
bols, or as the English names of these symbols : — 

a Alpha t] Eta - v Nu r Tau 

^ Beta (9 Theta ^ Xi v Upsi'lon 

y Gamma i Iota o Omi'cron <^ Phi 

8 Deha K Kappa tt Pi y^ Chi 

e Epsi'lon A Lambda p Rho \\j Psi 

^ Zeta /x Mu cr Sigma co Omeg'a 

A few constellations embrace more than 24 stars requir- 
ing especial designation, and for these the letters of the 
Latin alphabet are employed ; and if these are exhausted, 
then ordinary Arabic numerals follow. Thus stars may 
be designated as F Tauri, 31 Aquarii, and so on. About 
100 conspicuous stars have other and proper names, mostly 
Arabic in origin : thus Vega is but another name for a 
Lyrae, Aldeb^aran for a Tauri, Merak for /3 Ursae Majoris. 
The lucid stars, or stars visible to the naked eye, are 
divided into six classes, called magnittides. Of the first 
magnitude are the 20 brightest stars of the firmament, 
and the number increases roughly in geometric proportion. 
Of the sixth magnitude are those just visible to the naked 
eye on clear, moonless nights. On page 423 are given 
the names of the brightest stars ; and from Plates iii and 
IV can be found their location in the sky. 

Convenient Maps of the Stars. — On the star maps given as Plates 
III and IV are shown all the brighter stars ever visible in the United 
States. In each plate the lower or dark chart is a faithful tran- 
script of the ^ unlanterned sky.^ and the upper map is merely a key to 
the lowTr. Notwithstanding their small scale, the asterisms are readily 
traceable from the dark charts, and the names of especial stars and 
constellations are then quickly identified by means of the keys. To 
connect the charts with the sky, conceive the celestial sphere re- 
duced to the size of a baseball. At its north pole place the center 
of the circular map (Plate Iii) ; and imagine the rectangular map 
(Plate iv) as wrapped round the middle of the ball, the central hori- 




Kky to Chart oi^ North Poi.ar Hkavkns. 

[Shows how the stars appear, in relation to North Horizon, at 8 p.m. during the month 

held at the top.] 




Pi,ATR.III.— Thk North Polar Heavens. 



Constellation Study 6i 

zontal line of the chart coinciding with the equator of the ball. Just 
as the maps, if actually applied to a baseball, would not make a perfect 
cover for it without cutting and fitting, so there will be found some 
distortion in comparing the maps with the actual sky, especially near 
the top and bottom of the oblong chart. Whatever the season of the 
year, the charts are easy to compare with the sky, by remembering that 
(for 8 P.iM.) Plate iii must be held due north, and the book turned so 
that the month of observation appears at the top of the round chart, or 
vertically above Polaris, which is near the center of the map. The 
asterisms immediately adjacent to the name of the month will then be 
found at or near the observer's zenith. Similarly wdth Plate iv : face 
due south, and at 8 p.m. stars directly under the month will be found 
near the zenith, and the oblong chart will overlap the circumpolar one 
about half an inch, or 30^. At the middle of the rectangular chart, 
under the appropriate month, are found the stars upon the celestial 
equator ; and at the bottom of the map, the constellations faintly visi- 
ble near the south horizon. Every vertical line on this chart coincides 
with the observer's meridian at eight o'clock in the evening of the 
month named at the top. If the hour of observation is other than this, 
allow two hours for each month ; for example, at 10 p.m. in November 
the stars underneath 'December' will be found on the meridian. 
Likewise Plate iii must be turned counter-clockwise with the lapse of 
time, at the rate of one month for two hours. If, for example, we 
desire to inspect the north polar heavens at 6 p.m. in December, we 
should hold the book upright, with November at the top. 

Constellations of Circumpolar Chart. — Most notable is 
Ursa Major, the Great Bear, near the bottom (Plate iii). 
Its seven bright stars are familiarly known in America 
as the ^Dipper,' and in England as ' Charles's Wain,' or 
wagon. Of these, the pair farthest from the handle are 
called 'the Pointers,' because a line drawn through them 
points toward the pole star, as the arrow shows. The 
Pointers are five degrees apart, and, being nearly always 
above the horizon, are a convenient measure of large 
angular distances. At the bend of the dipper handle is 
Mizar, and very near it a faint star, Alcor. When Mizar 
is exactly above or below Polaris, both stars are on the true 
meridian, and therefore indicate true north (page 116). 
The Pointers readily show Polaris, a second magnitude star 



62 The Stars in their Courses 

(near the center of Plate in). No star of equal brightness 
is nearer to it than the Pointers. From Polaris a line of 
small stars curves toward the handle of the Dipper, meet- 
ing the upper one of a pair of the third magnitude. This 
pair, with another farther on and parallel to it, form the 
' Little Dipper,' Polaris being the end of its handle. The 
group is Ursa Minor. Opposite the handle of the great 
Dipper, and at about the same distance from Polaris, are 
five rather bright stars forming a flattened letter W. They 
are the principal stars of Cassiopeia. 

Learning the Constellations. — With these slender foun- 
dations, once well and surely laid, familiarity with the 
northern constellations is soon acquired. It is excellent 
practice to draw the constellations from memory, and then 
compare the drawings with the actual sky. An hour's 
watching, early in a September evening, will show that 
the Dipper is descending toward the northwest horizon, 
and Cassiopeia rising from the northeast. Nearly over- 
head is Vega. Capella, the large star near the left of 
Plate III, will soon begin to twinkle low down in the north- 
east. Familiarity with the northern constellations is the 
prime essential, and they should be committed, independ- 
ently of their relations to the horizon at a particular time; 
for at some time of the year all these constellations will 
appear inverted. Make acquaintance with them so thor- 
ough that each is recognized at a glance, no matter what 
its relation to the horizon may be. 

Constellations of the Equatorial Girdle. — All the more 
important ones are named on the key to Plate iv. None 
is more striking than Orion, whose brilliance is the glory 
of our winter nights. Hard by is Sirius, brightest of all 
the stars of the firmament, which, with Procyon and the 
two principal stars of Orion, forms a huge diamond, inter- 
sected by the solstitial colure, or Vlth hour circle. East- 



xxiv'^ 




Kky to Chart oi^ Equa 

[The stars under the name of the mont 



NOVEMBER I OCTOBER I SEPTEMBER I AUGUST I JULY 



JUNE 




PI.ATK IV.— The; Equai 




i^ GiRDivK o^ THK Stars. 

n the meridian (looking south) at 8 p.m.] 



I APRIL I MARCH I FEBRUARY I JANUARY I DECEMBER I NOVEMBER 




I, GiRDi^E OF the; Stars. 



Constellation Study 



63 



ward from Procyon to Regulus may be formed a vast 
triangle; and still farther east, with Spica and Arcturus, 
one vaster still. By means of similar arbitrarily chosen 
figures, as in the key, all the constellations may readily 
be memorized, one after another, until the cycle of the 
seasons is complete. Also the ecliptic's sinuous course 
is easy to trace, from Aries round to Aries again. 




Astral Lantern for tracing Constellations 



Helps to Constellation Study. — Perhaps the easiest to use and in 
every way the most convenient is the planisphere. By its aid all the 
visible constellations may be expeditiously traced, the times of rising 
and setting of the sun, planets, and stars found, and a variety of simple 
problems neatly solved. Another excellent help in learning the con- 
stellations is the astral lantern devised by the late James Freeman 
Clarke. The front side of the box is provided v^ith a ground glass slide. 
In front of and into the grooves of this may be slipped cards, figured 
with the different asterisms, as indicated in the illustration. But the 
peculiar effectiveness of the lantern consists in the minute punctures 
through the cards, the size of each puncture being graduated according 
to the magnitude of the star. Bailey's astral lantern is a similar device 



64 The Stars m their Courses 

for a like purpose. Also a celestial globe is sometimes used in learning 
the constellations, but the process is attended with much difficulty 
because the constellations are all reversed on the surface of the globe, 
and the observer must imagine himself at the center of it and looking 
outward. Plainly marked upon the globe are many of the circles of 
System (i5), — equator, colures, and parallels of declination. Also usu- 
ally the ecliptic. See illustration on page 71. The globe turns round in 
bearings at the poles, fastened to a heavy meridian ring m m which can 
be slipped round in its own plane through slots in the horizon circle H. 
The process of setting the globe to correspond to the aspect of the 
heavens at any time is called rectifying the globe. Bring the meridian 
ring into the plane of the meridian, and elevate the north pole to an 
angle equal to the latitude. On pages 70, 71, and 72 are globes recti- 
fied to the latitudes indicated. 

Farther Helps. — If complete knowledge of the firmament is desired, 
a good star atlas is the first essential, such as have been prepared with 
great care by Proctor, and Klein, and Sir Robert Ball, and Upton. 
These handy volumes quickly give a famiharity with the nightly sky 
which hurries the learner on to the possession of a telescope. By a 
list or catalogue of celestial objects may be found any celestial body, 
though not mapped in its true position on the charts, if an equatorial 
mounting like the model illustrated on page 53 is constructed. A 
mere pointer in place of the tube will make it into that convenient 
instrument called Rogers's ^star finder.' The simplest of telescopes 
must not be despised for a beginning. Astro7ioniy with an Opera 
Glass, by Serviss, shows admirably what may be done with the slight- 
est optical aid. When a 3-inch telescope becomes available, there is a 
multitude of appropriate handbooks, none better than Proctor's Half 
Hours with the Stars. Follow it with Webb's Celestial Objects for 
Co)n7Jio7i Telescopes, a veritable storehouse of celestial good things. 

The Zodiac. — Imagine parallels of celestial latitude as 
drawn on either side of the ecliptic, at a distance of 8° 
from it ; this belt or zone of the sky, 16° in width, is called 
the zodiac. Neither the moon nor any one of the bright 
planets can ever travel outside this belt. About 2000 
years ago both ecliptic and zodiac were divided by Hip- 
parchus, an early Greek astronomer, into twelve equal 
parts, each 30° in length, called the signs of the zodiac. 
The names of the constellations which then corresponded 
to them have already been given in their true order on 



The Zodiac 



65 



page 40; but the lapse of time has gradually destroyed 
this coincidence, as will be explained at the end of Chap- 
ter VI. In the figure the horizontal ellipse represents the 
ecliptic, and at the beginning of each sign is marked its 
appropriate symbol. E is the pole of the ecliptic, P 
the north celestial pole, and the inclined ellipse shows 
where the equator girdles the celestial sphere. The signs 




Celestial Sphere and Signs of the Zodiac 

of the ecliptic girdle have from time immemorial been 
employed to symbolize the months and the round of sea- 
sons ; and a type of ancient Arabian zodiac is embossed 
on the cover of this book, reproduced from Flammarion. 
The signs of the zodiac are discarded in the accurate 
astronomy of to-day ; and the positions of the heavenly 
bodies are now designated with reference to the ecliptic, 
not by the sign in which they fall, but by their celestial 
todd's astron. — 1; 



66 



The Stars in their Courses 



longitude. Conventionalized symbols of the signs of the 
zodiac, and the position of the zero point of each sign, 
are shown on the sphere on the preceding page, beginning 
with o"^ of Aries at D^ and proceeding counter-clockwise 
as the sun moves, or contrary to the direction the arrow. 

How to locate the Equinoxes among the Stars. — On 
the earth the longitude of places is reckoned from prime 
meridians passing through well-known places of national 



^\C)/ BETA 

fc/^ASSIOPElAE 






,---4^^, 




/ 


CASSIOPEIAE ^^^ 


7: 


/ SQUARE 
/ / OF PEGASUS 
jj^LPHERATZ 


O 


/ 


^^^ 


CLUSTER 
N PERSEUS 




■^^^^. 



VERNAL 




How to locate the Vernal Equinox 

importance. But the equinoctial colure, the prime merid- 
ian of the heavens, is a purely imaginary circle, and is not 
marked in any such significant manner, as we should nat- 
urally expect, by means of brilliant stars. It is, however, 
important to be able to point out the equinoxes roughly 
among the stars. The vernal equinox is above the hori- 
zon at convenient evening hours in autumn and winter. 
Its position may be found by prolonging a line (hour circle) 
from Polaris southward through Beta Cassiopeiae, as in 
the above illustration. 



How to Locate the Ecliptic 67 

This will be about 30'' in length. Thirty degrees farther in the 
same direction will be found the star Alpheratz (Alpha Andromedae), 
equal in brightness with Beta Cassiopeiae. Then as the equinox is a 
point in the equator, and the equator is 90° from the pole, we must go 
still farther south 30° beyond Alpheratz ; and in this almost starless 
region the venial equinox is at present found. It will hardly move 
from this point appreciably to naked-eye observation during a hundred 
years. This quadrant of an hour circle (from Polaris to the vernal 
equinox) will be very nearly a quadrant of the equinoctial colure also. 
Because Alpheratz and Beta Cassiopeiae are very near it, their right 
ascension is about o hours. Through spring and summer the autumnal 
equinox will be above the horizon at convenient evening hours. This 
equinox, like the other, has no bright star near it ; roughly it is about 
f of the way from Spica (Alpha Virginis) westward toward Regulus 
(Alpha Leonis), as shown in the following diagram. 













^-^^ 












Kv.t '» 
























\ 












^..^-^EGULUS 






§ 

z 
a 


• / 


^.^ 




CELESTIAL 


e 


cr^ 




EQUATOR 




© 

"-"^ SPiCA 




< 

z 

3 







SOUTH HORIZON 

How to locate the Autumnal Equinox 



How to locate the Ecliptic (approximately) at Any Time. 

— It will add much to the student's interest in these purely 
imaginary circles of the sky if he is able to locate them 
(even approximately) at any time of the day or night. 
Only two points in the sky are necessary. By day the 
sun is a help, because his center is one point in the ecliptic. 
If the moon is above the horizon, that will be another 



68 The Stars in their Courses 

point, approximately. Then imagine a plane passed 
through sun and moon and the point of observation, and 
that will indicate where the ecliptic lies. Also, if the 
moon is within three or four days of the phase known 
as the 'quarter,' her shape will show very nearly the direc- 
tion of the ecliptic in this manner : Join the cusps by 
an imaginary line, and the perpendicular to this line, 
extended both ways, will mark out the ecliptic very nearly. 
In early evening, the problem is easier. On about half 
the nights of the year the moon will afford one point. 
Usually one or more of the brighter planets (Venus, Mars, 
Jupiter, Saturn) will be visible, and it has already been 
shown how to distinguish them from the brightest of the 
fixed stars. Like the moon, these planets never wander 
far from the ecliptic ; and if we pass our imaginary plane 
through any two of them, the direction of the ecliptic may 
be traced upon the sky. 

If moon and planets are invisible, the positions of known stars are 
all that we can rely upon, and there are few very bright stars near the 
ecliptic. The Pleiades and Aldebaran (Alpha Tauri) are easy to find 
all through autumn and winter, and the ecliptic runs midway between 
them. Through winter and spring, the ^sickle' in Leo is prominent, and 
Regulus (Alpha Leonis) is only a moon's breadth from the true eclip- 
tic. Through the summer Spica (Alpha Virginis) is almost as favor- 
ably placed ; and Antares (Alpha Scorpii) rather less so, but not 
exceeding lo moon breadths south of the ecliptic. And in late sum- 
mer and autumn, Delta Capricorni, much fainter than all those pre- 
viously mentioned, shows where the ecliptic lies through a region 
almost wholly devoid of very bright stars. As the stars before named 
are so set in the firmament that at least two of them must always be 
above the horizon, they show approximately where the ecliptic lies. 

Finding the Latitude. — Having shown how the stars 
and constellations may be learned in our latitudes, it is 
next necessary to find how their courses seem to change, 
as seen from other parts of the earth. It is plain that 
going merely east or west will not alter their courses. 



Latittuic Equals Altitude of Pole 



69 



The effect of changing one's latitude must therefore be 
ascertained. Observe Polaris : attention has already been 
directed to the fact that in middle northern latitudes, as 
the United States, it is about halfway up from the north- 
ern horizon to the zenith. The true north pole of the 
heavens is 1° 15', or two and a half moon breadths from 
it. If you had a fine in- 
strument of the right kind, 
and the training of a skill- 
ful astronomer, you could 
measure accurately the 
altitude of the pole star 
w^hen exactly below the 
pole. Measure it again 
12 hours later, and it would 
be directly above that point. 
The average of the two 
altitudes, with a few slight 
but necessary corrections, 
would be the true altitude of the center of the little circle in 
which the pole star seems to move round once each day. 
This center is the true north celestial pole ; and whatever 
its altitude may be found to be, a facile proof by geome- 
try shows that it must be equal to the north latitude of the 
place where the observations w^ere made. 

Latitude equals Altitude of Pole. — Whether the earth 
is considered a sphere or an oblate spheroid, the angle 
which the plumb-line at any place makes with the terres- 
trial equator is equal to the latitude (figure above). As 
the plane of celestial equator is simply terrestrial equator- 
plane extended, the declination of the zenith is the same 
angle as the latitude. Now^ consider the two right angles 
at the point of observation ; {a) the one between celestial 
equator and pole, and {b) the other between horizon and 




Latitude equals Altitude of Pole 



JO The Stars in their Courses 

zenith : the angle between pole and zenith is a common 
part of both. So the declination of the zenith is equal 
to the altitude of the pole. Therefore the altihtde of the 
pole at aiiy give 71 place is equal to the latitude of that place. 
Going North the Pole Star rises. — If, then, one were 
to go north on the surface of the earth i"^, the pole of the 
northern heavens must seem to rise 1°. For example, if 
the latitude is 42°, one would have to travel due north 48° 
(3300 miles) in order to reach the north pole of the earth. 
^ And as the altitude of the 

, ^. ^ celestial pole would have in- 

creased 48° also, evidently 
this point and the zenith 

V \ "^^ would exactly coincide. To 

H^IR X '■ — — '^'^^.il^H all adventurous explorers who 

may ever reach the north 

pole, we may be sure that the 

^""^^^^^^^^^^WM pole star will be all the time 

very nearly overhead, and 
travel round the zenith once 
every day in a small circle 
J^ whose diameter would require 

'm about five moons to reach 

across. All other stars would 

Parallel Sphere (at the Poles) 

seem to travel round it m 
circles parallel to it and to the horizon also. This peculiar 
motion of the stars as seen from the north pole was the 
origin of the term pa7'allel spliere. 

Daily Motion of the Stars at the North Pole. — At the 
north pole the directions east and west, as well as north, 
vanish, and one can go only south, no matter what way 
one may move. As seen from the north pole, the stars all 
move round from left to right perpetually, in small circles 
parallel to the horizon. Consequently they never rise or 




Daily Motion of the Stars 



71 



set. All visible stars describe their own almucantars once 
every day. Their altitudes are constant, and their azimuths 
are changing uniformly with the time. The azimuths of all 
stars change with equal rapidity, no matter what their 
declination may be. These are the phenomena of the 
parallel sphere. All the stars north of the equator are 
always above the horizon, day and night. None of those 
south of the equator can ever be seen. If the observer 
were at the south pole of our globe, the daily motion of 
the stars relatively to the 
horizon would be exactly the 
same as at the north pole ; 
but they would all seem to 
travel round from right to 
left. The stars of the hemi-H| 
sphere which could be seen 
all the time would be those 
w^hich from the north pole 
could never be seen at all. 

Daily Motion of the Stars 
in the United States. — We 
have now returned from the 
north polar regions to middle 
latitudes, or N. 45°, about that 
of places from Maine to 
Wisconsin. The pole has gone down, too, and is elevated 
just 45° above the horizon ; consequently the circle of per- 
petual apparition, or parallel of north declination which is 
tangent above the north horizon, has shrunk to a diameter 
of 90° on the sphere. Any star ever seen between the 
zenith and the north horizon can never set. Similarly 
the circle of perpetual occultation must be 90"^ in breadth : 
it is the parallel of south declination which is tangent 
below the south horizon. Therefore the breadth of the 




Oblique Sphere TNorthern U. S.) 



72 



The Stars 171 their Courses 




Circles of Perpetual Apparition and Perpetual 
Occultation 



middle zone of stars, 
partly above and 
partly below the hori- 
zon, is 90°. The quad- 
rant from the zenith 
to the south horizon 
is the measure of its 
breadth when above 
the horizon, and the 
distance from the 
north horizon to the 
nadir is its width when 
below the horizon. 
As at the arctic circle, 
so here — the celes- 
tial equator marks the middle of the zone. All the 
stars in the northern half of it are visible longer than 
they are invisible, and the farther north they are, the 
longer they are above the 
horizon. In the same way 
all the stars of this zone 
whose declination is south 
are invisible longer than 
they are visible, and the 
greater their south declina- 
tion, the longer they are 
below the horizon. It has 
now been shown how the 
apparent motions of the stars 
are accounted for by the 
geometry of the sphere. 

Daily Motion of the Stars 
at the Equator. — Here our 
latitude is zero ; and as the Rj^ht sphere (at Equator) 




Equatorial at Different Latittcdes 



n 



altitude of the north celestial pole is always equal to the 
north latitude, the north pole must now be in the horizon 
itself. As the poles are i8o° apart, evidently the south 
pole of the heavens must now be in the south horizon. 
The equator, then, must pass through the zenith, and the 
stars can rise, pass over, 

and set, in vertical planes ' "' ~~ ' 

only, whence the name 
right sphere. A star's 
diurnal circle, therefore, 
is coincident with its 
parallel of declination. 
But what is now the 
size of the circles of per- 
petual apparition and 
occultation } It is evi- 
dent that they must 
have shrunk in dimen- 
sions more and more as 
we journeyed south. 
The circle of perpetual 
apparition is now a mere 
point, — the north pole 
itself ; and the circle of 

perpetual occultation is a point also, — the south pole. 
No star, then, can be visible all the time, nor can any 
be invisible all the time. The equatorial zone of stars, 
visible part of the time and invisible the remainder of 
each day of 24 hours, has expanded to embrace the entire 
firmament. Every star, no matter what its declination, is 
above the horizon 12 sidereal hours and below it 12 hours, 
and so on alternately forever. 

The Equatorial at Different Latitudes. — Remembering 
that the principal axis of the equatorial telescope must 




Equatorial at the Poles 



74 



The Stars in their Courses 



always be directed toward the pole of the heavens, it is 
easy to see what the construction of the instrument must 
be, to adapt it for use in different latitudes. At the pole 
itself, were an equatorial telescope required for that lati- 
tude, the polar axis 
would be vertical (pre- 
ceding page); and the 
equatorial would not 
differ at all from the 
altazimuth. As we 
travel from the pole 
into lower latitudes, 
the polar axis is tilted 
from the vertical ac- 
cordingly ; until at the 
equator it becomes ac- 
tually horizontal, as 
illustrated adj acent. 
An equatorial mount- 
ed at middle latitudes 
has already been 
shown on page 53. 
It must not be thought that this change of latitude and cor- 
responding inclination of the polar axis modifies in any 
way the relations of other parts of the equatorial. The 
polar axis is always in the meridian; and its altitude, 
or the elevation of its poleward end, is always equal to 
the latitude. The polar axes of equatorial telescopes 
in all the observatories of the world are parallel to one 
another. 




Equatorial at the Equator 



Large equatorial mountings, or those rigid enough to carry a tele- 
scope above six inches aperture, always have the frame or pier head 
cast by the maker in such form that the bearing for the polar axis shall 
stand at the angle required by the latitude of the place where the tele- 



Equatorial at Different Latitudes 75 

scope is to be used ; smaller instruments, called portable equatorials, 
generally have the bearing of the polar axis attached to the pier, stand, 
or tripod, by means of a rigid clamp ; the polar axis can then be tilted 
to correspond to any required latitude, as shown by a graduated quadrant 
or otherwise. Such portable, or universal, equatorials are an essential 
part of the equipment of eclipse and other astronomical expeditions. 
As the polar axis is reversed, end for end, in passing from one hemi- 
sphere to the other, the clockwork motion must be reversible also, 
because the stars move from east to west in both hemispheres. 

Our next inquiries are directed toward the astronomical 
relations of the earth on which we dwell, its form and size, 
and the elementary principles by which these facts are 
ascertained. 



/^ 



CHAPTER V 

THE EARTH AS A GLOBE 



THE original idea of the earth, as given in the Homeric 
poems, was that of an immense, flat, circular plane, 
around which Oceanus, a mythical river, not the 
Atlantic, flowed like a vast stream. It was thought to 
be bounded above by a hollow hemisphere turned down- 
ward over it, through and across which the heavenly 
bodies coursed for human convenience and pleasure. 

Ancient Idea of the Earth. — Anaximander (b.c. 580) re- 
garded the earth as a flat, circular section of a vertical 
cylinder, with Greece and the Mediterranean surrounding 
the upper end. Herodotus (b.c. 460), whose geographic 

knowledge was exten- 
'"^^^"^ -^^-^^___-_^_^_ .^^ ^j^^^ ridiculed the idea 

of a flat and circular 
earth. To Plato (b.c. 
390), the earth was a 
cube. Even as late as a.d. 550, Cosmas drew the earth as 
a rectangle, twice as long (east and west) as it was broad 
(north and south), from which conception have originated 
the terms longitude (length) and latitttde (breadth); and 
from the four corners of this rectangular earth rose pillars 
to support the vault of the sky. The venerable Bede (a.d. 
700) promulgated the theory of an egg-shaped earth, float- 
ing in water everywhere surrounded by fire. Long before 
this, however, Thales (b.c 600) and Pythagoras (b.c 530) 
had taught that the earth was spherical in form ; but the 

76 



c^ 

Curvature of the Ocean exaggerated 



The Cnrv attire of the Earth 



77 




Ship's Rigging Distinct, Water Hazy 



erroneous beliefs persisted through century after century 

before the doctrine 

of a globular earth 

was fully established. 

Final doubt was 

swept away by the 

famous voyage of 

Magellan, one of 

w^hose ships first 

circumnavigated the 

globe in the i6th 

century, and in three 

years returned to its 

starting point. 

How to see the Cur- 
vature of the Earth. 

— By ascending to greater and greater heights above the 

earth's surface, the horizon retreats farther and farther. 

If we ascend a peak 
in mid-ocean, the ex- 
tension of the radius 
of vision may be seen 
to be the same in 
every direction, thus 
indicating a spherical 
earth. But a better 
experimental proof 
may be had. Near 
the shore of a large 
body of water, on a 
fine day when ships 
can be seen far out, 
mount a telescope (as 

indicated opposite) upon a high building or cliff. The 




Water Distinct, Rigging Ill-defined 



78 



The Earth as a Globe 



intervening water will be imperfectly seen (page Jj\ but 
the ship's masts and rigging well defined, if all conditions 
are favorable. Now draw out the eyepiece of the tele- 
scope until the waves on the horizon line appear sharply 
defined. The details of the ship will then be hazy and 
indistinct, because the ship is farther away than the water 
which hides her hull. Repeat the observation by focusing 
the telescope alternately on the ship and the water in the 
same field of view, — affording ocular proof that the 
earth's surface curves away from the line of vision. 
Wherever this simple experiment is tried, the result will 
be the same ; so we reach the conclusion that the earth is 
round like a ball. 






DENVER 



CHICAGO 



NEWjYORK 



Earth a Plane, Local Time everywhere the Same 



Telegraphic Proof that the Earth is Round. — Farther 
proof that the earth is not a plane may be derived with 
the assistance of the electric telegraph. If the earth were 
a plane, local time would everywhere be the same. This 
condition is shown in the above figure, for Denver, Chi- 
cago, and New York : the lines of direction in which the 
sun appears from all three places are parallel, because 
the distance separating them is not an appreciable part 
of the sun's true distance. Therefore, as the sun's angle 
east of the meridian corresponds to lo a.m. at one place, 



Measurement of the Earth 



79 



it should be lo a.m. at all. But at lo a.m. at Chicago, if 
the operator asks New York and Denver what time it is 
at those places, he will receive the answer that it is 9 
o'clock at Denver and 1 1 at New York. The sun, there- 
fore, must be 15° east of the meridian at New York, as 
shown in the figure below, 30° at Chicago, and 45° at Den- 
ver. So the meridian planes of these three places cannot 
be parallel, as in the first illustration, but must converge 
below the earth's surface, as shown in the second one. 

By means of land lines and cables, the local time has been compared 
nearly all the way round the globe, eastward from San Francisco to 
New York, across the Atlantic Ocean, over the eastern hemisphere, 
through Europe and Asia to Japan. Everywhere it is found that 




Earth a Globe, Local Time depends on the Longitude 

meridians converge downward in such a way that all would meet in 
a single line. This geometric condition can be fulfilled only by a 
solid body, all of whose sections perpendicular to this common line 
are circles. Therefore the earth is round, east and west; and, by 
going north and south in different parts of the earth, and continually 
observing the change in meridian altitudes of given stars, it is found 
that the earth is round in a north and south direction also. But all 
these curvatures as observed in different places nearly agree with each 
other; therefore, the earth is nearly a sphere. 

History of the Measurement of the Earth. — While the 
Chaldeans are credited with having made the first esti- 



8o The Earth as a Globe 

mate of the earth's circumference (24,000 miles), the 
Greeks, beginning with Aristotle (b.c. 350), made note- 
worthy efforts to solve this important problem, which is 
preliminary to the measurement of all astronomical dis- 
tances. Eratosthenes (b.c. 240) and Cleomedes (a.d. 150) 
applied the gnomon to the measurement of degrees on 
the earth's surface, and devised the application of geom- 
etry to this problem essentially as it is employed to-day. 
They made Syene 7° 12' south of Alexandria; and as the 
measurement of distance between these places made them 
5000 stadia apart, the proportion 

7°.2: 360°:: 5000: — 

gave for the circumference of the earth 250,000 stadia, or 
24,000 miles. 

Posidonius (b.c 260) made a similar determination between Rhodes 
and Alexandria. Early in the ninth century of our era, the Arabian 
caliph Al-Mamun directed his astronomers to make the first actual 
measurement of an arc of a terrestrial meridian, on the plain of Singar, 
near the Arabian Sea. Wooden poles were used for measuring rods, 
but the result is uncertain, because the details of the corresponding 
astronomical observations are not known. Fernel, in France, measured 
a terrestrial arc early in the i6th century, adopting a method like that 
of Eratosthenes, and beginning that brilliant series of geodetic meas- 
ures which, through succeeding centuries, did much to establish the 
scientific prestige of France. Also Picard measured an accurate arc of 
meridian in 1671, used by Newton in establishing his law of gravitation. 

Geodesy. — Geodesy is the science of the precise meas- 
urement of the earth. Accurate geodetic surveys have 
been conducted during the present century in England, 
Russia, Norway, Sweden, Germany, India, and Peru ; and 
eventually the transcontinental measurements, completed 
in the year 1897 by the United States Coast and Geodetic 
Survey, will make a farther and highly important contri- 
bution to our knowledge of the size and figure of the earth. 
Evidently an arc of a latitude parallel may make additions 



Eartlis Size and Volume 8i 

to this knowledge, as well as an arc of meridian. In the 
former case the astronomical problem is to find the differ- 
ence of longitude between the extremities of the measured 
arc ; in the latter, the corresponding difference of latitude. 
The processes of geodesy proper — that is, the finding out 
how many miles, feet, and inches one station is from 
another — are conducted by a system of indirect measure- 
ments called triangulation. 

Triangulation. — Although Ptolemy (a.d. 140) had shown that an 
arc of meridian might be measured without going over every part of it, 
rod by rod, the first application of his important suggestion was made 
by Willebrord Snell, a Netherland geometer of the 17th century. 
Trigonometry is the science of determining the unknown parts of 
triangles from the known. When one side is known and the two 
angles at its ends, the other sides can always be found, no matter what 
the relative proportions of these sides. It is evident, then, that if a 
short side has been measured, the long ones may be found by the much 
simpler, less tedious, and more accurate process of mathematical calcu- 
lation. Triangulation is the process of finding the exact distance 
between two remote points by connecting them by a series or network 
of triangles. The short side of the primary triangle, which is actually 
measured, foot by foot, is called the base. For the sake of accuracy 
the base is often measured many times over. Thenceforward, only 
angles have to be measured — mostly horizontal angles ; and this part of 
the work is done with an altazimuth instrument. We must pass over 
the explanation of the somewhat complex process of getting the single 
desired result from a rather large mass of observations and calcula- 
tions. The base must not be too short ; and the stations must be so 
selected as to give well-conditioned triangles. Of course an equilateral 
triangle is wTll-conditioned in the extreme, and good judgment is re- 
quired in deciding how great a departure from this ideal figure is allow- 
able. The triangle on page 235, with the earth^s diameter as a base, 
is exceedingly ill-conditioned. SnelPs base was measured near Leyden ; 
but it was shorter than it should have been ; the telescope was not then 
available for accurate measurement of angles ; and some of his triangles 
were ill-conditioned, consequently his result for the size of the earth 
was erroneous. The geometers of to-day employ the principles of his 
method unchanged, but with great improvement in every detail. 

Earth's Size and Volume. — As a result of such labors, it 
is found that the length of the shortest diameter of the 

TODD'S ASTRON. 6 



82 



The Earth as a Globe 



earth, or the distance between the two poles, is 7900 miles. 
In the plane of the equator, the diameter of our globe is 
7927 miles, or about 3^-^-^ part greater than the diameter 

through the poles. 
This fraction is a 
little less than the 
oblateness of the 
earth or its polar 
compression. Re- 
cent measurements 
indicate that the 
equator itself is 
slightly elliptical, 
but this result is not 
yet absolutely estab- 
lished. The form of 
the earth may there- 
fore be regarded as 
an ellipsoid with 
three unequal diam- 
eters, or axes. Know- 
ing the lengths of 
these diameters, the 
volume of the earth 
has been calculated 
and found to be 260 billion cubic miles. As the size of 
the earth was first determined by measuring the length 
of a meridian arc, and comparing it with the difference of 
latitude at the two ends of the arc, we next describe an 
easy method of finding the latitude. 

How to observe the Latitude. — It is probable that you 
can take the latitude of the place where you live, more 
accurately from the map in any geography, than you can 
find it by the method about to be described. But the 




The Latitude-box in Position 



How to Observe the Latitude 



83 



principle involved is often used by the astronomer and 
navigator, and it is important to understand it fully, and 
to test it practically, although there may be at hand no 
instrument better than a plumb-line and a pasteboard 
box. 

A box about six or seven inches square should be selected. The 
depth of the box is not important — four or five inches will be con- 




venient. Cut a hole \ inch square {A) through the middle of one 
side, at the bottom. On the inside paste a piece of letter paper over 
this hole, as indicated by the dotted hne CB (opposite page). Trans- 
fer a duplicate of the above graduated arc to a stiff sheet of highly 
calendered paper or very smooth bristol board about four inches 
square. Trim the little quadrant accurately, taking especial care that 
the edges of it at the right angle shall exactly correspond with the 
lines. The quadrant is now to be pasted on the inside of the bottom 
of the box, in such a way that the center of the arc, or the right-angled 
point, will be in contact with the bit of paper pasted over the aperture. 



84 



The Earth as a Globe 



One thing more, and the latitude-box is complete : exactly opposite the 
right-angled apex of the quadrant, and perhaps a sixteenth of an inch 
away from its plane, pierce a pin hole through the letter paper. Now 
select a window facing due south, and tack the box on the west face 
of its casing, so that the quadrant will be nearly in the meridian. 
The illustration on page 82 shows how it should be fastened. Put in 
a tack at F. Then hang a plumb-line by a fine thread in front of the 
box, and sight along it, turning the box round the tack until the line 

ED is parallel to the 
plumb-line. Then tack 
in final position at G^ and 
verify the direction of ED 
by the plumb-line after- 
wards. The latitude-box 
is now ready for use. 

To make the Observa- 
tion. — On any cloudless 
day, about half an hour 
before noon, the sunlight 
falling through the pin 
hole will inake a bright 
elongated image at H. 
As the sun approaches 
nearer and nearer the 
meridian, this image will 
travel slowly toward A", 
becoming all the time less 
bright, but more elongate. Just before apparent noon it will appear as 
a light streak, A7L, about one degree broad, and stretching across the 
graduation of the quadrant. The observation is completed by taking 
the reading of the middle of this light streak on the arc, to degrees 
and fractional parts as nearly as can be estimated. It is better to set 
down this reading in degrees and tenths decimally. 

To calculate or reduce the Observation. — Only a single prin- 
ciple is necessary here, because in our latitudes refraction by the air 
(page 91) will never be an appreciable quantity. Take the sun's dec- 
lination from table on following page. The above diagram shows 
how it should be applied to the reading on the arc. If declination 
is south, subtract it from the reading on arc of the quadrant, and 
remainder is the latitude. But if sun's declination is north, add it to 
the quadrant reading, and the sum will be equal to the latitude. The 
quadrant reading is sun's zenith distance; and the -single principle 
employed is the fundamental one : that the altitude of the pole (or 
declination of zenith) is equal to the latitude. 




Latitude equals Zenith Distance plus Declination 



Finding Accurate Latitude 



85 



The Sun's Declination. — The sun's declination is its 
an2:ular distance either north or south of the celestial 
equator. It varies from day to day, and may be taken 
from the following table, with sufficient accuracy for the 
foregoing purpose during the years 1897- 1900. 

The Sun's Declination at Apparent Noon 



Day 


Decl. 


Day 


Decl. 


Day 


Decl. 


Jan. I 


23^0 S. 


May I 


I5°.2 N. 


Aug. 


29 


9°.2N. 


II 


21 .7 S. 


II 


18 .oN. 


Sept 


8 


5.5N. 


21 


19 .8 S. 


21 


20 .3 N. 




18 


I .6 N. 


31 


17 .2 S. 


31 


22 .0 N. 




28 


2 .2 S. 


Feb. 10 


14 .2 s. 


June 10 


23 .0 N. 


Oct. 


8 


6.1 S. 


20 


10 .7 S. 


20 


23 .5 N. 




18 


9 .8 S. 


Mar. 2 


7.0S. 


30 


23 .2 N. 




28 


13 .3 S. 


12 


3.1 s. 


July 10 


22 .2 N. 


Nov. 


7 


16 .5 S. 


22 


.8N. 


20 


20 .6 N. 




17 


19 .1 S. 


Apr. I 


4.7N. 


30 


18 .4N. 




27 


21 .2 S. 


II 


8 .5 N. 


Aug. 9 


15 .7N. 


Dec. 


7 


22 .7 s. 


21 


12 .0 N. 


19 


12 .6N. 




17 


23 .4 s. 


May I 


15 .2N. 


29 


9 .2N. 




27 


23 .3 s. 



The values are adjusted to every tenth day through the 
year. Find the value for any intermediate date pro- 
portionally. 

How the Latitude is found accurately. — But while a 
crude method like the foregoing has a certain value as 
illustrating the outline of a principle, it is of no impor- 
tance to the astronomer, because of the impossibility of 
eliminating the very large errors to which it is subject. 
He therefore employs a variety of other methods. The 
best is the method of equal zenith distances. 

The instrument for measuring them is called the zenith telescope. 
Two stars are selected whose declinations are such that one of them 



86 



The Earth as a Globe 



culminates as far north of zenith as the other does south of it. The 
telescope is constructed with a delicate level attached to its tube, so that 
it can be clamped rigidly at any angle. When the first star is observed 
set the level horizontal: then turn the instrument round 180'^, taking 

care not to disturb the level. The second, 
star will cross the field of view, because 
the telescope will now be pointing as far 
on one side of zenith as it was on oppo- 
site side in the first position. Declina- 
tions of both stars must be accurately 
known ; and these, with small corrections 
depending upon instrument and atmos- 
phere, give the means of calculating lati- 
tude with great precision. The zenith tel- 
escope is usually a small instrument, per- 
haps 3 feet high. The one here shown is 
employed by DooHttle at the Flower 
Observatory of the University of Pennsyl- 
vania, in making the critical observations 
described at the end of this chapter. At 
fixed observatories the latitude is generally 
Zenith Telescope determined by means of the meridian 

(Warner & Swasey) circle (described on page 216). 




Length of Degrees of Latitude and Longitude. — The 

length of a degree on the equator is 69^ statute miles. 
At the equator a degree of longitude and a degree of 
latitude are very nearly equal in length, the latter being 
only about -:^-^ part longer. Leaving the equator, degrees 
of longitude grow rapidly shorter, because meridians 
converge toward the pole. In latitude 30° the degree of 
longitude has shrunk to 60 miles, so that a minute of longi- 
tude is covered for every mile traveled east or west. In 
the United States, average length of a minute of longitude 
is I- of a mile. 



By measuring degrees of meridian at various latitudes, they are found 
invariably longer, the nearer the pole is approached. So curvature of 
meridians must decrease toward the pole, because the less the curvature 
of a circle, the longer are degrees upon it. The figure opposite shows 



Terrestrial Gravity 



87 



NO. 


POLE 






90^ 


eo^ 








~-L°° 







/ 


r^\6o 












~ / 





/ Q / \50 ' 


eo 




/ 


/ '^ /o X40° 


>< 


/ 


/ 


/ / "^ r& A30° 


'J': 




k 




W 




Equator j 



Degrees grow Longer 
toward the Poles . 



this effect much exaggerated, but actual differences are not large ; at 
equator the length of a degree of latitude is 68^, in the United States 
almost exactly 69, and at the pole 69} miles. 
The angle between equator-plane and a line 
from any place to earth's center is called its 
geocentric latitude ; and the difference be- 
tween it and ordinary or geographic latitude 
is the angle of the vertical. It is zero at poles 
and equator, and amounts to about 11' at lati- 
tude 45°, geocentric being always less than 
geographic latitude. 

Terrestrial Gravity. — By gravity 
is meant the natural force exerted on 
all terrestrial matter, drawing or tend- 
ing to draw it downward in the direc- 
tion of the plumb-line. All objects, as air, water, buildings, 
animals, earth, rock, metals, are held in position by this 
attraction, and it gives them the property called weight. 
As we know, if the earth were dug away from under us, we 
should fall to a point of rest nearer the earth's center. If 
gravity did not exist, all natural objects not anchored firmly 
to earth would be free to travel in space by themselves. 
The ultimate cause of this force has not yet been ascer- 
tained, but its law of action has been fully investigated 
(page 384). It diminishes as we go upward, being a thou- 
sandth part less on a mountain 10,000 feet high. Gravity 
remains constant at a given place, and is exerted upon all 
objects alike. If unobstructed, all fall to the earth from a 
given height in exactly the same time. 

Try the experiment for yourself, using two objects to which the air 
offers very different resistance — a silver dollar, and a piece of tissue 
paper about half an inch square. Hold the coin delicately suspended 
horizontally between thumb- and finger. Practice releasing the coin so 
that it will remain horizontal while dropping. Then place the paper 
lightly on top of the coin. The paper will fall in exactly the same time 
as the coin does, because the coin has partially pushed the air aside, 
and permitted gravity to act upon the paper, quite unhampered by 



88. The Earth as a Globe 

resistance of the atmosphere. The coin pushes the air aside and falls 
as quickly as the paper falls without pushing the air aside. But the fall 
of the coin is not appreciably delayed by aerial resistance, and both 
coin and paper fall through the same distance in the same time. 

The Earth's Form found by Pendulums. — If a delicately 
mounted pendulum of invariable length is carried from 
one part of the globe to another, it is found from com.pari- 
son with timepieces regulated by observations of the stars, 
that its period of oscillation, or swinging from one side 
of its arc to the other, is subject to change. Richer first 
tested this in 1672. By carrying from Paris to Cayenne 
a clock correctly regulated for the former station, he found 
that it lost 2m. 28s. a day at the latter ; and it was necessary 
to shorten the pendulum accordingly. Now, conversely, 
preserve the length of the pendulum absolute, and record 
the exact amount of its gain or loss at places differing 
widely in latitude and longitude; then it will be possible 
to find their relative distance from the center of the earth, 
because the law connecting the oscillation of the pendulum 
with the force of gravity at different distances from the 
earth's center is known. At the sea level in the latitude 
of New York, a pendulum oscillating once a second is 39. i 
inches long, and the times of vibration of pendulums vary 
as the square root of their lengths. This kind of a survey 
of the earth is called a gravimetric survey, and opera- 
tions in the process are termed swinging pendtihims. 

In this manner it has been ascertained that the force of gravity at 
the earth's poles must be about y^^ greater than at the equator. But 
in order to find the earth's figure, this result must be corrected because 
the effect of the earth's attraction is everywhere (except at the poles) 
lessened on account of the centrifugal force of its rotation. It is great- 
est at the equator, amounting to ^\^. Subtracting this from j^q, the 
remainder is about -^l^ . This result makes the earth's equatorial 
radius about 13^ miles longer than its polar radius, thereby verifying the 
value derived from the measures of meridian arcs. Pendulum observa- 



Weighing the Earth 



89 



tions can be made at numerous localities where the contour of the 
surface is so irregular that measurement of arcs is impracticable. Be- 
sides this, the swinging of pendulums has revealed many interesting 
facts regarding the earth's crust ; important among them being this — 
that the mountains of our globe are relatively light, and some of them 
mere shells. American geometers who have contributed most to these 
researches are Peirce and Preston. 

Weighing the Earth. — The mass of the earth is six 
thousand millions of millions of millions of tons. Per- 
haps this statement does not assist 
very much in reaHzing how heavy \ 

the earth actually is ; but it may 
arouse interest in regard to methods 
of reaching such a result. Several 
have. been employed, but the bare 
outline of the first one ever tried is 
indicated by the figure of a section 
of the earth surmounted by a rather 
abrupt mountain. The straight lines 
drawn downward (one from the 
north and the other from the south 
side of the mountain) converge 
toward the center of the earth. 
Outward toward the stars each line 
would point in the direction of the 
zenith of the station a or b, if the 
mountain were not there. But the 
attraction of the mountain mass 
draws toward itself the plumb-lines 
suspended on both sides of it ; so 
that the difference of latitude of the two stations is made 
greater by the amount that the angle of the dotted lines 
exceeds the angle at the center of the earth. But the 
true difference of latitude between a and b can be found 
by surveying round the mountain. This survey, too, must 




Weighing the Earth 



90 



The Earth as a Globe 



be so extended that the volume of the mountain may be 
ascertained ; geologists examine its rock structure, and its 
actual weight in tons is calculated. Then by a mathe- 
matical process the earth is weighed against the mountain, 
and the result in tons given above is obtained from the 
ratio of the mass of our globe to the mass of the moun- 
tain. Schiehallion in Scotland was the mountain first util- 
ized in this important research, about a century ago. As 
a result of all the measures of different methods, the 
earth's mean density is found to be 5.6. This means that 
if there were a globe entirely composed of water and of 
exactly the same volume as our globe, the real earth would 
weigh 5.6 times as much as the sphere of water. 

Atmospheric Refraction. — The earth is completely sur- 
rounded by a gaseous medium called the atmosphere. 

Even when perfectly tran- 
quil, the atmosphere has 
a remarkable effect upon 
the motion of a ray of 
light in bending it out of 
its course. Two proper- 
ties true of all gases are 
concerned in atmospheric 
refraction — weight and 
compressibility. The atmosphere is probably at least 100 
miles in depth ; and gravity attracts every portion of it 
vertically downward. Its total weight is about 5 x 10^^ 
(five quadrillions = 5,000,000,000,000,000) tons, or y2 o^ioTo 
that of the entire earth. Conceive the atmosphere divided 
into layers concentric round the earth and one another, 
as above. The lowest shell must support not only the 
weight of the shell next outside it, but of all the other 
shells still beyond. Evidently, then, as the atmosphere 
is compressible, the force of gravity renders successive 




Refraction increases the Apparent Altitude 



Law of Refraction 



91 



strata more and more dense as the surface of the earth 
is approached. The greater the density, the more the re- 
fraction ; so that lower strata bend, or refract, rays of Hght 
out of their course more than upper layers do. 

Law of Refraction. — According to the law of refraction, 
rays of light from any celestial body striking the air in the, 
direction of the plumb-line, 
will pass downward along 
that line undeviated ; but any 
rays impinging on the atmos- 
phere otherwise than verti- 
cally — that is, rays from 
celestial bodies whose zenith 
distance is not zero — will be 
refracted more and more 
from their original course, 
the nearer they are to the 
horizon. The less the alti- 
tude, the greater the refrac- 
tion ; and, as an object always seems to be in that direc- 
tion from which its rays enter the eye, refraction elevates 
the heavenly bodies, or makes their apparent altitude 
greater than their true altitude. The figure shows how 
refraction varies from zenith to horizon. 




Refraction at Different Altitudes 



If the altitude is 45°, the refraction is 58'', or nearly one minute of 
arc ; but so rapidly does the density of the atmosphere increase near 
the earth's surface that the refraction at zenith distance 85° is 9' 46", 
more than 10 times greater than at 45°; and increase in the next five 
degrees is even more rapid, so that the refraction at the horizon is 
34' 54^'. A correction on account of refraction must be calculated 
and applied to nearly all astronomical observations. Generally ther- 
mometer and barometer must both be read, because cold air is denser 
than warm, and a high barometer indicates increase of pressure of the 
superincumbent air. In both these instances the amount of refraction 
is increased. To determine how much the refraction was at the time 
when an astronomical observation was made at a given altitude, and to 



92 The Earth as a Globe 

apply the corresponding correction suitably, is part of the work of the 
practical astronomer. It is greatly facilitated by means of elaborate 
Refraction Tables. 

Effects of Atmospheric Refraction. — The angular breadth 
of the sun is, as we shall see, about one half a degree ; and 
as this is nearly the amount of atmospheric refraction at 
the horizon, evidently the sun is really just below the sensi- 
ble horizon when at its setting we still see it just above 
that plane. And as the diurnal motion of the celestial 
sphere carries the sun over its own breadth in about two 
minutes of time, refraction lengthens the day about four 
minutes, in the latitude of the United States ; this effect 
being much increased as higher latitudes are reached. It 
is easy to see, also, that the sun must be continually 
shining on more than an exact half of the earth, refrac- 
tion adding a zone about 40 miles wide extending all the 
way round our globe, and joining on the line of sunrise 
and sunset. Farther effects of atmospheric refraction are 
apparent in those familiar distortions of the sun's disk 
often seen just before sunset. Refraction elevates the 
lower edge, or limb, more than the upper one, so that 
the sun appears decidedly flattened in figure, its vertical 
diameter being much reduced — an effect far more pro- 
nounced in winter than in summer. 

Scintillation of the Stars. — Scintillation or twinkling 
of the stars is a rapid shaking or vibration of their light, 
caused mainly by the state of the atmosphere, though 
partly as a result of the color of their intrinsic hght. 
That the atmosphere is a cause of twinkling is evident 
from the fact that stars twinkle more violently near the 
horizon, where their rays come to us through a greater 
thickness of air. 

Also the stars t\vinkle more in winter than in summer ; and very vio- 
lent scintillations often afford a o^ood forecast of rain or snow. Marked 



Twilight 93 

twinkling of the stars is an indication that the atmosphere is in a state 
of turmoil — currents and strata of different temperatures intermingling 
and flowing past one another. The astronomer describes this state of 
things by saying that the 'seeing is bad.' Consequently, high magni- 
fying powers cannot be advantageously used with the telescope. A 
star's light seems to come from a mere point, so that when its rays are 
scattered by irregular refraction, at one instant very few rays reach the 
eye, and at another many. This accounts for the seeming changes of 
brightness in a twinkling star. Ordinarily the bright planets are not 
seen to twinkle, because of their large apparent disks, made up of a 
multitude of points, which therefore maintain a general average of 
brightness. At a given altitude white or blue stars (Procyon, Sirius, 
Vega) twinkle most, yellow stars (Capella, Pollux, Rigel) a medium 
amount, and red stars (Aldebaran, Antares, Betelgeux) least. 

Twilight, — At a particular and definite instant of con- 
tact with the sensible horizon, the sun's upper edge comes 
into view at sunrise and disappears at sunset. But long 
before sunrise, and 
a corresponding ^ 

time after sunset, 
there is an indirect 
and incomplete il- 
lumination diffused 
throughout the at- 
mosphere. This is 

called tWl hgh t. j^e zone of Twilight in Midwinter 

Morning twilight is 

generally called dawn. In part twilight is due to sunlight 
reflected from the upper regions of the earth's atmosphere. 
As twilight lasts until the sun has sunk i8° below the 
horizon, evidently its duration in ordinary latitudes must 
vary considerably with the season of the year. But the 
variation dependent upon latitude itself is greater still. 
A vast twilight zone nearly 1500 miles wide completely 
encircles the earth. 

This zone, ABEFm the figure, is continually slipping round as our 
globe turns on its axis. One edge of it, along the line of sunrise and 




94 The Earth as a Globe 

sunset, is constantly facing the sun. At the equator, where the sun's 
daily path is perpendicular to the horizon, the earth turns through this 
zone of twilight in about i \ hours. In the latitude of the United States, 
the average length of twilight exceeds i^ hours, its duration being 
greatest in midsummer, when it is more than two hours. At the 
actual poles of the earth, twilight is about 2\ months in duration. If 
the earth had no atmosphere, there would be no twilight ; the blackness 
of night would then immediately follow the setting of the sun. 

The Aurora. — The aurora borealis (often called the 
northern lights) is a beautiful luminosity, striated and 
variable, seen at irregular intervals, and only at night. 
From the general latitude of the United States, it appears 
as a soft vibrating radiance, streaming up most often into 
the northern sky, occasionally as far as the zenith, but 
usually in a semicircle or arch extending upward not over 
30°. Its probable average height is about 75 miles. The 
aurora, generally greenish yellow in color, has occasionally 
been seen of a deep rose hue, as well as of a pale blue, and 
other tints. The continual vibration, sometimes the rapid 
pulsation, of its streamers, gives it a character of mystery 
only too well enhanced by our lack of knowledge of its 
causes. That these are connected with the magnetism 
of the earth is certain ; also that a strong influence upon 
the magnetic needle is somehow exerted. Telegraph in- 
struments and all other magnetic apparatus are greatly 
disturbed when auroras are brightest. This wonderful 
spectacle grows more frequent and pronounced, as the 
north pole is approached ; and is closely connected, though 
in a manner incompletely understood, with the period of 
sun spots, and the protuberances. When there are many 
sun spots, auroras are most frequent and intense. Proba- 
bly they are merely an electric luminosity of very rare 
gases. 

The spectrum of the aurora is discontinuous (page 272), and far 
from uniform. Always there is one characteristic green line, all others 



The Wandering Terrestrial Poles 95 

being faint, and varying from one auroral display to another. At times 
there appear to be two superposed spectra. A similar phenomenon in 
the southern hemisphere is sometimes called aurora aiistralis ; also the 
general term aurora polaris is often applied to the aurorae of both 
hemispheres. 

The Wandering Terrestrial Poles. — Referring back to 
the remarkable photograph of stars around the northern 
celestial pole (page 33), we recall the fact that the center 
of all these arcs is that pole itself. And we may farther 
define the terrestrial north pole as that point in the earth 
directly underneath this celestial pole, or that point on our 
globe where the center of this system of concentric arcs 
would appear to be exactly in the zenith. But without 
actually going there, how can astronomers determine the 
precise position of this point on the earth's surface, and so 
find out whether it shifts or not t Evidently by finding as 
closely as possible, at frequent intervals of time, the lati- 
tude of numerous places widely scattered over the world. 
If the latitude of a place, Berlin, for example, is found to 
increase slightly, while that of another place on the oppo- 
site side of the globe, as Honolulu, decreases at the same 
time and by the same amount, the inference is that the 
position of the earth's axis changes slightly in the earth 
itself. So definite are the processes of practical astronomy 
that the position of the north pole can be located with no 
greater uncertainty than the area of a large Eskimo hut. 
Nearly all the great observatories of the world are fully 
3000 miles from this pole ; still if this important point 
should oscillate in some irregular fashion by even so slight 
an amount as three or four paces, the change would be 
detected at these observatories by a corresponding change 
in their latitude. Such a fluctuation of the pole has actu- 
ally been ascertained, and it affects a large mass of the 
observations of precision which astronomers and geode- 



96 



The Earth as a Globe 



sists have made in the past. Technically it is called the 
variation of latitude. 

Only recently recognized, the physical cause of it is not yet fully es- 
tablished. But the nature and amount of it are already pretty well made 
out. Around a central point adjacent to the earth's north pole, draw a 
circle 70 feet in diameter, as shown in the illustration. Within this cir- 
cle the pole has always been since the beginning of 1890. Its wander- 
ings from that time onward to the beginning of 1895 are clearly indicated 

by the irregularly curved 
line which has been care- 
fully laid down from a 
discussion of a large 
number of accurate ob- 
servations of latitude at 
13 observatories located 
in different parts of the 
world. Let the eye trace 
the curve through all its 
windings, and the mean- 
ing of the oscillation, or 
wandering of the north 
pole, will be appreciated. 
From the beginning of 
1890 to January, 1894, 
the curve seems to have 
been roughly an in-wind- 
ing spiral, the pole going 
round once in about 14 
months. The latitudes of all places on the globe change by corre- 
sponding amounts. Chandler of Cambridge first brought clearly to 
light the variation of latitude, and American investigation of it has 
been farther advanced by Preston, Doolittle, and Rees. This move- 
ment of the pole is not yet well enough understood to enable astrono- 
mers to predict its future movements ; but it seems probable that they 
will be confined within the narrow limits here indicated. 




Observed Wandering^ of the North Pole 



Were the earth at perfect rest in space, its poles would 
not partake of this remarkable motion, in part dependent 
upon a slow turning round on its axis. The next chapter 
is concerned with this fundamental relation, of the utmost 
significance in astronomy, both theoretic and practical. 



CHAPTER VI 

THE EARTH TURNS ON ITS AXIS 

SO far we have dealt only with the seeming motions of 
the heavenly bodies about us ; in ancient times these 
were regarded as their actual motions. The glory 
of the sun by day, and all the magnificence of the nightly 
firmament were considered accessory to the earth on which 
men dwell. Till the time of Copernicus our abode was 
generally believed to be enthroned at the center of the 
universe. Now we know, what is far less gratifying to our 
self-importance, that this earth is only one — a very small 
one, too — of the vast throng of celestial bodies scattered 
through space, somewhat as moving motes in a sunbeam. 
All the stately phenomena of the diurnal motion, the 
appearances we have been studying, are easily and natu- 
rally explained by the simple turning completely round 
of our little earth on its axis once in a given period of 
time. This the ancient world naturally divided unevenly 
into day and night ; but the astronomers of a later day, 
more philosophically, divide it into 24 hours, all of equal 
length, and this division is the only one recognized at the 
present day. 

In the Dome of the Capitol. — Imagine yourself in the rotunda, or 
directly under the center of the dome of the Capitol at Washington. 
Turn once completely round from right to left, meanwhile observing 
the apparent changes in the objects and paintings on the inner walls of 
the dome. Just above the level of the eye, you face, one after another, 
all the twelve historical paintings exhibited in the rotunda. Turning 
todd's astron. — 7 97 



98 The Earth Turns on its Axis 

round again at the same speed as before^ the pillars half way up, appar- 
ently much reduced in size from their greater distance, seem to move 
more slowly. Turning round the third time, with the eyes directed 
still higher, the outer figures in the colossal painting at top, the ceil- 
ing of the dome, appear to turn more slowly still ; w^hile if you w^atch 
attentively the very apex of the dome, the central point of Constantio 
Brumidi^s famous fresco will seem to have no motion whatever. This 
very simple experiment can be tried quite as effectively in the middle 
of any ordinary square room, first imagining its corners drawn inward, 
roughly to represent a dome. Seat yourself on a revolving piano stool 
or a swivel chair, and, as you turn slowly round from right to left, watch 
the apparent motion of pictures on the wall, figures in the frieze, and 
spots on the ceiling. To confine the direction of vision look through 
a pasteboard roll, or other handy tube, elevating it to different alti- 
tudes as desired. Now it would be ridiculous to insist that the dome 
(or even the room) is turning around you, thereby causing these 
changes, while you are at rest in the center. Yet this was precisely 
the explanation of the apparent movement of the heavens accepted 
by the ancient world, false as it was, and very im.probable as it would 
in our age seem to be. While the true doctrine of the rotation of the 
earth was held and taught by a few philosophers from very early times, 
it was not universally accepted till the downfall of the Ptolemaic system. 

The Direction in which the Earth turns. — When riding 
swiftly through the street in a carriage or a car, it is quite 
easy, by imagining yourself at rest, to see, or seem to see, 
all the fixed objects — houses, shops, lamp-posts, and so 
on — rushing by just as swiftly in the opposite direction. 
Although you may be going east, you seem to be station- 
ary, and they appear to travel west. While looking at the 
paintings in the Capitol (or the engravings on the wall) in 
succession as you turned round from right toward left, they 
appeared to be going just opposite — from left toward right. 
Now simply conceive all these objects to be moved outward 
in straight lines from the point of observation, each in the 
direction in which it lies, to a distance indefinitely great 
as if along the spokes of a vast wheel, whose hub is at the 
eye, but whose tire reaches round the heavens. When re- 
moved to a distance sufficiently great, we may imagine them 



The Earth Turns Eastzvard 99 

to occupy places in the sky which some of the celestial 
bodies do. But we have seen that sun, moon, and stars all 
move in general from east to west, so we reach the easy 
and natural conclusion that our earth is turning over from 
west toward east. Once this cardinal fact of the earth's 
turning eastward on its axis is established and accepted, 
there is a full explanation of that apparent westward drift 
of which all the heavenly bodies, sun, moon, and stars in 
common, partake. Also the natural succession of day and 
night is robbed of its ancient mystery. ^^ 

Proof that the Earth turns Eastward. — Quite independently of 
its point of suspension, a pendulum tends to swing always in that plane 
of oscillation in which it is originally set going. Suspend any con- 
venient object, weighing one or two pounds, by a fine thread attached 
to the center of a stick or ruler. Hold it in both hands, and set the 
pendulum swinging in the plane of the stick. Then, without raising 
or lowering it, quickly swing the ruler quarter way round its center in a 
horizontal plane. The pendulum keeps on swinging in the same plane 
as before, although it is now at right angles to the ruler. Repeat the 
experiment several times, until you succeed in moving the stick without 
changing the position of its center, and it will be seen that the ruler 
may be swung, either slowdy or rapidly, into any position whatever, 
without aflfecting the plane of the pendulum's motion appreciably. 
Now imagine the short thread replaced by a very fine wire 200 feet 
long, suspending a ball weighing 70 or 80 pounds ; and in place of the 
ruler turned round by hand substitute the Pantheon at Paris, turned 
slowly round in space by the earth itself. These are the conditions of 
this celebrated experiment as tried in 1851 by Foucault, a French 
physicist, who thereby provided ocular proof that the earth turns 
round from west toward east. He set the pendulum swinging in the 
plane of the meridian, but it did not long remain so. The south end 
of the floor being nearer the equator than the north end, it traveled 
eastward a little faster than the north end did, so that the floor turned 
counter-clockwise underneath the swinging pendulum. Therefore, the 
plane of oscillation appeared to swing round clockwise. This experi- 
ment has been repeated in different parts of the earth, and always with 
the same result. The four figures on the next page show the varying 
conditions. In the southern hemisphere the pendulum appears to turn 
round counter-clockwise. As for the rate of turning, at either pole it 
makes a complete revolution in the same time that the earth does, and 



lOO 



The Earth Ttcrns on its Axis 




the time of revolution grows greater and 
greater as the latitude grows less. Exactly 
on the equator, the plane of oscillation does 
not change at all with reference to the 
meridian. 



In Northern Latitudes 




In Southern Latitudes 



Day and Night. — Granted the 
rotation of the earth on its axis, and 
the alternation of day and night is 
fully and clearly explained. The 
Sim may even remain fixed among 
the stars of the celestial vault. By 
the earth's turning round, all places 
upon its surface, as New York, 
Chicago, and San Francisco, are 
carried into the sunshine and out 
of it alternately. From the dark- 
ness of night there comes, first, the 
dawn, with twilight growing brighter 
and brighter, then sunrise, followed 
by the sim rising higher and higher, 
till it reaches the meridian. Then 
it is midday, or noon. Afterward 
the order of occurrence is reversed, 
— noon, afternoon, simset, twilight, 
night again. All these phenomena 
are, in a general way, connected 
by everybody with lapse of time, and 
progress of the hours from night to 
noon, and from noon back to night 
again. Uniform turning of the globe 
in the figure opposite makes this rela- 
tion obvious. Count of the hours 
At the Equator is bcgim at o or 12, when the sun is 

Foucaults Experimental Proof highest, and COUtinUCd tO 12, whcn 

of Earth's Rotation ^ ' ' 




At the North Pole 




Day and Night at the Eqtiinoxes loi 

the sun is lowest ; and if earth were transparent as crystal, 
the sun could be seen through it at midnight — cross- 
ing the lower meridian as far beneath the northern horizon 
at midnight, as it was above the southern horizon at noon. 
Day and Night at the Equinoxes. — The ecliptic has 
been defined as the yearly path of the sun round the 
heavens. As it hes at an angle of 23|-° to the celestial 
equator, at some time each year the sun's declination 
must be 23|-° south, and six months from that time 
its declination must be 231^"^ north. Midway between 




Alternation of Day and Night 

these points, the sun will be crossing the equator; 
that is, its declination will be zero, and the sun's center 
will be at those points of intersection of equator and 
ecliptic, called the equinoxes. Why they are so called 
will be apparent from the figure above given ; for the 
sun is on the celestial equator, because the earth's equa- 
tor-plane extended would pass through it. The great cir- 
cle of the globe which separates the day hemisphere from 
the night hemisphere, exactly coincides with a terrestrial 
meridian. Everywhere on that meridian it is 6 o'clock 
— 6 o'clock A.M. on the half which the globe by its turn- 
ing is ca:rrying round toward the sun, and 6 o'clock p.m. 
on the other half which is being carried out of sunlight. 



I02 



The Earth Turns on its Axis 



It is sunrise everywhere on the former half of this meridian, 
and sunset everywhere on the latter half. As daytime is 
the interval from sunrise to sunset, and night-time is the 
interval from sunset to sunrise, the day and the night are 
each 12 hours in length, and therefore equal. Whence 
the term equinox^ from the two Latin words that give us 
our English words equal and night. This equality of day 

and night all over the 
world occurs only twice 
each year. When the sun 
is crossing the equator and 
going northward, this hap- 
pens about the 2ist of 
March ; and going south- 
ward, about the 2ist of 
September. 

Day and Night at the 
Solstices. — From March to 
September, the sun is north 
of the celestial equator. Therefore, at our middle lati- 
tudes he is among the stars that are above the horizon 
longer than they are below it, as the upper figure on 
page 72 clearly shows. During this period of the year, 
daytime in north latitudes is always longer than the night- 
time immediately preceding or following it. At the sum- 
mer solstice the sun's declination has reached its maximum, 
or 23^-'^. The days then will be as long as possible, and the 
nights as short as possible. From September to March, on 
the other hand, the sun is south of the celestial equator, and 
therefore among the stars that are below the horizon longer 
than they are above it. During these months, then, night- 
time in our hemisphere is always longer than daytime. At 
the winter solstice the sun's declination is again a maximum, 
but it is 23^^ south or about midway between E and S. So 




Diurnal Circles in Middle South Latitudes 



Day and Night at Equator 



103 



that the days are then shortest, and the nights longest. But 
these relations of day and night to the different months are 
true for the northern hemisphere only. 



Day and Night South of the Equator. — The opposite figure has been 
suitably modified from the one on page 72, in order to show the relation 
of day and night at diiterent times of the year for places of middle south 
latitude. By holding the page in a vertical plane, and looking west as 
you read, the diagrams will better correspond to actual conditions. 
For every degree of latitude that you pass over, in traveling southward, 
the north pole of the heavens goes down one degree, and the south 
pole rises one degree. The diagram opposite is adapted to south lati- 
tude 45°, much farther south than either Capetown, Valparaiso, or Mel- 
bourne. The south pole of the heavens is now as far above the south 
horizon as it was below the south 
horizon, in a place of equal north 
latitude ; and the relations of 
daytime to night-time are corre- 
spondingly reversed. From Sep- 
tember to March, therefore, when 
the sun's declination is south, the 
sun is among the stars that are 
above the horizon longer than 
they are below it ; so that the 
daytime always exceeds the 
night. From March to Sep- 
tember, the sun being in north 
declination, the daytime clearly 
is shorter than the night. If at 
any time of the year we com- 
pare the length of the day at a 
given north latitude with the 
length of the night at an equal 
south latitude, we shall find them 
equal. Also the converse of this 
proposition is true. 

Day and Night at the Earth's Equator. — We have considered the 
relation of day to night at middle north latitudes ; and the explanation 
given holds good for all places in the United States. Also the oppo- 
site relations, which obtain in south latitudes. It remains to consider 
the effect at the equator. Recalling the fact that the latitude of a 
place is always equal to the altitude of the visible pole of the heavens, 
it is clear that if the place selected is anywhere on the earth's equator. 




Diurnal Circles at the Equator 



I04 The Earth Ttirns on its Axis 

both celestial poles must be visible and coincide with the north 
and south points of the horizon (figure on preceding page). The 
horizon, then, must coincide with the celestial meridians, or hour circles, 
one after another as they seem to pass by it, in consequence of the 
apparent motion of the celestial sphere; and ever}^ star's diurnal circle 
is the same as its parallel of declination. But every hour circle divides 
parallels of declination in half: therefore, every star of the celestial 
sphere, as seen from a station on the earth's equator, is above the 
horizon 12 hours and below it 12 hours. Clearly this is tme no 
matter what the star's declination may be ; therefore it must always be 
true of the sun, although its declination is all the time changing. Had 
the early peoples who invented our astronomical terms lived upon the 
equator where day and night are always equal, the term equinox would 
not have signified anything unusual, and a different word would have 
been necessary to define the time when, and the point where, the sun 
crosses the celestial equator. 

Sunrise and Sunset. — Refer to any ordinary almanac. 
The times of sunrise and sunset are given usually for two 
or three definite cities, north and south, or for zones of states 
varying widely in latitude. These are local mean times 
when the upper edge or limb of the true sun, as corrected 
for refraction, is in contact with the sensible horizon of 
the place, or of any place of equal latitude. The local 
time will not often coincide with the standard time, now 
almost universally used. But the correction required is 
simply dependent upon the difference between the longi- 
tudes of the place and of the standard meridian. If you 
are west of the standard meridian, for each degree add 
four minutes to the almanac times ; if east, subtract. In 
verifying the almanac times by observation, remember the 
difference between sensible and apparent horizons. 

Almanac Sunrise and Sunset at the Equinoxes. — We have seen 
that when the sun — that is, the sun's center — is on the equator, it rises 
at the same time everywhere, and that time is 6 o'clock. So. too, it sets 
everywhere at 6 o'clock. Why, then, do the times predicted in the 
almanacs differ from this? The reason is threefold, {a) The times of 
sunrise and sunset are all corrected for refraction, which at the horizon 
amounts to nearly o°.6, or more than the sun's own breadth. As re- 



The Midnight Sun 105 

fraction always increases the apparent altitude of celestial bodies, 
the sun can be seen wholly above the horizon when really below it. 
Therefore this effect alone lengthens the daytime about five minutes, 
causing the refracted sun to rise about two and one half minutes earlier 
than the true sun, and set about the same amount later, (b) The 
almanac times of sunrise and sunset refer to the upper edge or limb of 
the sun. not the center. Here, again, is a cause operating in like man- 
ner with the refraction, but with an effect about half as great, {c) The 
almanac times are mean solar times of the rising and setting of the real 
sun. This difference between true sun and fictitious sun also displaces 
the times of sunrise and sunset, by the amount of the equation of time 
(page 112) : at the vernal equinox the sun is six minutes slow^ ; at the 
autumnal equinox, eight minutes fast. All three effects when combined 
at the vernal equinox, delay the sunset until long after six, and cause 
the sun to rise at the autumnal equinox long before six. 

Sunrise and Sunset in Different Latitudes. — Compare 
the almanac times of sunrise and sunset in different lati- 
tudes on the same day. At the end of the third week 
of March, the times of sunrise are practically the same, 
no matter what the latitude. So are the sunset times. 
Through April, May, and June, the farther north, the 
earlier is sunrise and the later is sunset ; the daytime is 
longer, and the night-time shorter. This difference on 
account of latitude increases until the third week in June ; 
then it slowly diminishes until sunrise and sunset again 
occur at the same time regardless of latitude, at the end of 
the third week in September. 

Through the remaining half of the year, a change of latitude affects 
the time of sunrise oppositely ; also the time of sunset : the farther 
north one goes, the later is sunrise, and the earlier is sunset. The 
daytime is shorter, and the night-time longer. As the year wears on, 
the latitude-difference of the times of both sunrise and sunset grows 
greater, until about Christmas time ; afterward it as gradually decreases 
until the vernal equinox. Then, go north or south as far as one may 
choose, the sun will rise at the same local time ; and sunset will be 
unaffected also. 

The Midnight Sun. —The farther north one travels, the 
higher the pole rises toward the zenith ; consequently a 



io6 



The Earth Turns on its Axis 



\ NORTHERN HORIZON / 



AT WASHINGTON 



NORTHERN HORIZON 



NORTHER N-^^C;;^:-'^ HORIZO 
AT ST. PETERSBURG 



NORTHERN HORIZON 
IN LAPLAND 



Midsummer Sun at 
Midnight 



latitude must after a while be reached where the midsum- 
mer sun, at and near the solstice, just grazes the north 
horizon at midnight, and so does not set 
at all. The daytime period, therefore, is 
24 hours long, and night-time vanishes." 
For the northern hemisphere, the northern 
parallel of 66^° is this latitude. The 
change in the sun's daily path will be 
apparent in referring to the illustration ; 
it shows how much shorter the sun's arc of 
invisibility below the horizon grows, as one 
travels north, from Washington to Paris, 
Saint Petersburg, and Lapland. Midnight 
sun is the popular name for the sun when 
visible in midsummer at its lower culmi- 
nation underneath the pole of the heavens. 
The entire period of 24 hours is all daytime, and there is 
no night. It occurs in high northern latitudes in June ; 
and similarly in high southern latitudes in December, the 
midsummer period of the southern hemisphere. The 
northern extremity of the Scandinavian peninsula is known 
as the ^ Land of the Midnight Sun,' because this weird and 
unusual phenomenon has been most often observed from 
that region. 

Length of Day at Different Latitudes. — For all places 
on the earth's equator there is never any inequality of day 
and night. The farther we go from the equator, either 
north or south, the greater this inequality, the longer 
will be the days of summer, and the nights of winter. 
Regarding the day geometrically as the interval of time 
during which the center of the sun is above the sensible 
horizon, it is easy to calculate the greatest length of the day 
at any given latitude. The results are as follows and they 
are true for latitudes either north or south of the equator : 



The Long Polar Night 107 

JVIaximum Length of Day at Different Latitudes 



At Latitude — 


Greatest Length of 
Day is — 


At Latitude — 


Greatest Length of 
Day is — 


0^.0 


12 h. 




Months 


30 .8 


14 


67°.4 


I 


49 -0 


16 


11> -7 


3 


58.5 


18 


84.1 


5 


63 .4 


20 


90 .0 


6 


65 .8 


22 






66.5 


24 







But these results are much modified by refraction of the 
atmosphere. At the time of greatest length of day in the 
northern hemisphere is occurring the greatest length of 
night in the southern hemisphere. 

The Long Polar Night. — Ordinary notions of the six months of the 
polar night need some correction. If the actual north pole were reached, 
it is true that the sun would really be below the horizon very nearly 
six months, that is from the 20th of September to the 20th of March, 
while it is south of the equator ; and imagining the earth to turn round 
on its axis inside of this atmosphere shell, as in the figure on page 93, it 
is clear how twilight at the pole under B continues throughout the en- 
tire 24 hours, so long as the pole is inclined away from the sun. But 
the duration of twilight, longer and longer as the pole is approached, is 
a very important factor not to be neglected. Supposing twilight to last 
till the sun is depressed 18° below the horizon, so long is the autumn 
twilight that its continuance for i\ months would postpone the begin- 
ning of deep night till about the ist of December; while the spring 
dawn, equally protracted, would begin early in January. Even at the 
pole, then, true night with an absolutely dark sky would be only six or 
seven weeks long. So much for the sun ; and fortunately for the arc- 
tic explorer, the moon helps wonderfully to alleviate this dreary period. 
As the sun is so far south, the crescent moon at old and new, being 
near it, will, like the sun itself, be below the polar horizon ; but during 
the fortnight from first quarter to last quarter, including the period of 
its full phase, it will shine continually above the horizon. As the moon 
must ^fuir at least twice during the i^ months when sunhght is wholly 
withdrawn, the period of absolute night is reduced to about three weeks 



io8 The Earth Turiis on its Axis 

at the most. And even this will now and then be broken by brilliant 
auroras, especially during years of prevalent sun spots. If one retreats 
from the pole only 5°, or to latitude 85° north, it is quite possible that 
the period of utter night may vanish entirely ; and, of course, still far- 
ther south, the number of hours of night illumined by neither sun nor 
moon must usually be exceedingly few. 

The Sidereal Day. — As referred to a fixed star, the 
period of rotation of the earth on its axis does not vary. 
One such rotation is called a sidereal day^ or day as re- 
ferred to the stars. It is subdivided into 24 sidereal hours, 
each hour into 60 sidereal minutes, and each minute into 
60 sidereal seconds. Every observatory possesses a clock 
regulated to keep this kind of time, and called a sidereal 
clock. The hours of sidereal time are always counted 
consecutively through the sidereal day from o to 24. 

Approximately in the meridian, as found from the sun by the method 
on page 23, suspend two plumb-lines from some rigid support which 
does not obstruct the view south. Secure the lower ends of the plumb- 
lines in the exact position where they come to rest, taking care to stretch 
the lines taut. As soon as the stars are out, observe and record the 
hour, minute, and second when some bright star is in line with both of 
them. Its altitude should not exceed 60° above the south horizon. 
Use the best clock or watch at hand. The next clear night, repeat the 
observation on the same star ; also on two succeeding evenings, setting 
down the day, hour, minute, and second in each case, and taking care 
that the running of the timepiece shall not be interfered with mean- 
while, nor the plumb-lines disturbed. On comparing these observa- 
tions it will be found that the star has been crossing the plumb-hnes 
about four minutes earlier each day. If the observations were to be 
continued on subsequent days, we should find only the same result, 
and so on indefinitely : the star w^ould soon come to the lines in bright 
twilight, and it could not be observed without a telescope. A few days 
later it would cross at sunset, and it is easy to calculate that in about 
three months it would cross at noon, star and sun culminating to- 
gether. By this simple method is established that cardinal element in 
astronomy, the period of the earth's turning round on its axis. Astrono- 
mers have, to be sure, much more accurate methods than this ; and the 
instruments employed by them are described and pictured in a later 
chapter, but only the details vary, the principle remaining the same. 



Telling Time by the Stars 



109 



Telling Time by the Stars. — Our next inquiry concerns 
the point that corresponds to o hours, o minutes, o seconds; 
that is, the beginning of the sidereal day. Having found 
this, our timepiece 
may be set to corre- zenith Q 

spond ; and if regu- ^ 

lated, it will continue 
to keep sidereal time. 
As sidereal time sus- 
tains a relation to the 
sun which is all the 
while varying, it is 
clear that the sidereal 
day may begin when 
any star is crossing 
the meridian ; but it 
is also clear that all 
astronomers should 
agree to begin the 
sidereal day by one 
and the same star, or 
reference point. This is practically what they have done ; 
and the point selected is the vernal equinox, often called 
*the First of Aries,' or 'the First point of Aries'; also 
sometimes, ' The Greenwich of the Sky.' 

The equinoctial colure passes through it ; and for all stars exactly 
between the vernal equinox and either celestial pole, the right ascension 
is zero, no matter what their declination may be. Fortunately there is 
a bright star almost on this line, and only 32° from the north pole ; so 
it is always above the horizon in our country, except for an hour or 
two each day, in some of the most southern states. This important 
star is Beta Cassiopeiae (page 66). When it is crossing the upper merid- 
ian, being as near as possible to the zenith, sidereal time is o h. o m. o s. 
and a new sidereal day begins. The relation of this conspicuous star to 
Polaris is shown in the above diagram. Surrounding both stars is 
drawn a clock-hand which may be imagined as turning round with the 




Telling the Sidereal Time by Cassiopeia 



1 1 o The Earth Turns on its Axis 

stars once each day. Very little practice is necessary to enable one to 
tell the sidereal time by the direction of this colossal clock-hand in the 
northern sky ; but one must never fail to notice that it moves oppositely 
to the hour hand of an ordinary watch, and only half as fast. At 6 h. 
it points toward the west horizon, and at i8 h. toward the east point of 
the horizon ; not horizontally, as represented in the figure, but down- 
ward in each case by a considerable angle varying with the latitude. 
Subtracting the ^ sidereal time of mean noon' (page 122), gives ordinary 
or solar time. This operation is called ' telling time by the stars ' — 
a method of course only approximate ; but an error greater than 1 5 
or 20 minutes will not often occur. 

The Apparent Solar Day. — It was shown (page 108) how 
to ascertain by observation that the sun seems to be con- 
tinually moving eastward among the stars. It was shown, 
too, that sidereal noon (noon by the stars) comes at all 
hours of the day and night during the progress of the 
year. Plainly, then, sidereal time is not a fit standard for 
regulating the affairs of ordinary life ; for, while it would 
answer very well for a fortnight or so, the displacement of 
four minutes daily would in six months have all the world 
breakfasting after sunset, staying awake all through the 
night, and going to bed in the middle of the forenoon. 
As the sun is the natural time-regulator of the engage- 
ments and occupations of humanity, he is adopted as the 
standard, although you will find by observing attentively 
that his apparent motion is beset with serious irregulari- 
ties. Begin on any day of the year, and observe the sun's 
transit of the meridian, as you did that of a star. The 
instant when the sun's center is on the meridian is 
known as apparent noon. If you repeat the observation 
every day for a year, and then compare the intervals 
between successive transits, you will find them varying 
in length by many seconds, because they are all apparent 
solar days ; they will not all be equal, as in the case of 
the star. 

The Mean Solar Day. — By taking the average of all 



Astronomical and Civil Day 1 1 1 

the intervals between the sun's transits, that is, the mean 
of all apparent solar days in course of the year, an invari- 
able standard is obtained, like that from the stars them- 
selves. In effect, this is precisely what astronomers have 
done, with great care and system ; and for convenience, 
they imagine an average, or mean, sun, called the ficti- 
tious sun, which they accept as their standard, and then 
calculate the difference between its position and that of 
the real sun which they observe. The fictitious sun may 
be defined as an imaginary point or star which travels 
eastward round the celestial equator, not the ecliptic, at 
a perfectly uniform rate, making the entire circuit of the 
heavens in course of the year. It is easy to see that the 
intervals between transits of the fictitious sun must all 
be equal; and obviously, too, this interval is longer than 
the sidereal day, for this reason : if a star and the ficti- 
tious sun should cross the meridian together on one day, 
then on the next day the star would come to the merid- 
ian first, thereby making the sidereal day shorter than 
the solar day. The instant when the center of the ficti- 
tious sun is on the meridian is called mean noon. The 
mean solar day, therefore, may be defined as the interval 
between two adjacent transits of the fictitious sun over the 
same meridian ; or the mean of all the apparent solar 
days of the year. It is divided into 24 mean solar hours, 
each hour into 60 mean solar minutes, and each minute 
into 60 mean solar seconds. This is the kind of hours, 
minutes, and seconds kept by clocks and watches in com- 
mon use. 

Astronomical and Civil Day. — The mean solar day is 
often called the astronomical day, because it begins at 
one mean noon and ends at the one next following. Its 
hours are counted continuously from o to 24, without a 
break at midnight. It is the day recognized by astronomers 



1 1 2 The Earth Turns on its Axis 

in observatory work and records, and by navigators in using 
the Nautical Almanac. The ordinary or civil day is ex- 
actly the same in length as the astronomical day, but it 
begins at the midnight preceding noon of a given astro- 
nomical day, and ends at the next following midnight. As 
every one knows, its hours are not usually counted con- 
tinuously from o to 24, but in two periods of 12 each. The 
hours of its first period are ante meridiem, that is, before 
midday, or a.m., and the hours of its second period are 
post meridiem, that is, after midday, or p.m. Therefore, 
civil time, p.m., of a given date is just the same as the 
astronomical time ; if a date recorded in astronomical time 
between midnight and noon is to be converted into civil 
time, it is necessary to subtract 12 from the hours and add 
I to the days. For example : — 

Civil Date Astronomical 

6 o^clock P.M., loth November, 1899 = 1899 November 10 d. 6 h. 
3 o'clock A.M., 15th December, 1899 = ^^99 December 14 d. 15 h. 

The astronomical date is always recorded in the philo- 
sophic order here given — year, month, day, hour, minute, 
second. 

The Equation of Time. — Ordinary clocks and watches 
are regulated to run according to the average, or fictitious, 
sun, which makes all the days of equal length ; the sun 
itself is sometimes ahead of this 'fictitious sun,' and some- 
times behind it. This deviation is called the equation of 
time, and the explanation of it is given in the next chapter. 
We shall soon need it (page 119) in ascertaining mean 
noon by observing the real sun's transit over the meridian. 
With sufficient accuracy for the years 1 897-1900 it is as 
follows : S meaning ' sun slow ' (that is, the center of the 
real sun does not cross the meridian until after mean 
noon), and F meaning * sun fast ' : — 



Rctardatio7i of Sicnsci 
The Equation of Time 



I I 





Day of 
Month 


JANL- 


\RY 


Febrl 


ARY 


March 


April 


May 


ju.e 




m. 


S. 


m. 


S. 




m. 


s. 


m. 


s. 


m. 


s.' 


m. s. 


I 


S 4 


7 


S13 


54 


S 


12 


23 


S3 


44 


F3 


6 


F2 21 


6 


S 6 


-J 


S14 


21 


s 


I I 


17 


S2 


16 


F3 


34 


F I 29 


II 


S 8 


26 


S14 


27 


s 


10 





So 


33 


F3 


49 


Fo 31 


i6 


S 10 


14 


S14 


14 


s 


8 


33 


Fo 


22 


F3 


49 


So 31 


21 


Sii 


44 


S13 


43 


s 


7 


3 


Fi 


29 


F3 


36 


S I 36 


26 


S 12 


S3 


S 12 


37 


s 


5 


34 


F2 


24 


F3 


9 


S 2 40 


31 


SI3 


46 


Sii 


58 


s 


4 


2 


F3 


6 


F2 


30 


S3 40 


Day of 
Month 


July 


August 


September 


October 


November 


December 




m. 


s. 


m. 


s. 




m. 


s. 


m. 


s. 


m. 


s. 


m. s. 


I 


S3 


40 


S6 


4 


F 





19 


F 10 


32 


F16 


19 


F 10 32 


6 


S4 


34 


S5 


37 


F 


I 


57 


F12 


3 


F16 


•3 


F 8 30 


II 


ss 


18 


S4 


SS 


F 


3 


40 


F13 


23 


FI5 


46 


F 6 16 


16 


S5 


51 


S3 


59 


F 


5 


25 


F14 


31 


FI4 


58 


F 3 52 


21 


S6 


10 


S2 


50 


F 


7 


II 


F15 


24 


FI3 


49 


F I 23 


26 


S6 


16 


Si 


30 


F 


8 


33 


F16 





FI2 


20 


S I 7 


31 


S6 


8 


So 


I 


F 


10 


32 


F16 


18 


Fio 


32 


S 3 33 





Retardation of Sunset near the Winter Solstice. — About 
Christmas time in our latitudes we may begin to look for 
the lengthening of the day, which betokens the return of 
spring. At first the increase is very slight, perhaps only 
two or three minutes in the course of a week. And it 
is commonly observed that the increase takes place in the 
afternoon half of the day ; that is, the sun sets later and 
later each day, although its time of rising does not show 
much change until the middle or latter part of January. 
The reason of this is that sunrise and sunset are calculated 
for the real sun ; but the times themselves are mean times, 
that is, time according to the fictitious sun. The real sun 

TODD'S ASTRON. — 8 



114 



The Earth Turns 07i its Axis 



is fast about five minutes in the middle of December, so 
that the afternoon is ten minutes shorter than the fore- 
noon. But the equation of time is diminishing rapidly ; 
that is, the real sun is moving eastward more rapidly than 
the fictitious sun, and will soon coincide with it, making 
the equation of time zero. On account of this eastward 
motion of the real sun, more rapidly than usual, its mean 

time of setting is re- 
tarded so much that the 
effect begins to be ap- 
parent as a lengthening 
of the day, even before 
the sun reaches the sol- 
stice. After the solstice 
is passed, the sun's dec- 
lination is less, and its 
longer diurnal arc con- 
spires with the rapid 
eastward movement of 
the real sun ; so that by 
the end of December 
both causes make the 
sun set a minute later 
each day. For a similar 
reason, operating at the 
summer solstice, the 
forenoon half of the day 
begins to' shorten as 
early as the middle of 
June. 

Time Keepers of the Ancients. — It is not known that the 
ancients had any clocks similar to ours ; but they meas- 
ured the lapse of time by clepsydras and sundials. Fre- 
quently also the gnomon, or pointed pillar, was used. 




Antique Form of Clepsydra 



To Find Trite North 1 1 5 

A clepsydra is a mechanical contrivance for measuring and indicating 
time by means of the flow of water. The illustration shows a common 
form. Water is supplied freely to the conical vessel, an overflow main- 
taining always a given level, so that the pressure at bottom is con- 
stant. Through a small aperture and pipe, the water drops into a 
larger cylindrical vessel which fills very slowly. On the surface of the 
water in it rests a float, attached to which is an upright ratchet rod. 
Working into the teeth of this are the teeth of a cog wheel, and on the 
same arbor with it is a single hand, which revolves round the dial and 
marks the progress of the hours. With a contrivance of this sort, time 
could be told within five or six minutes. The day of the ancients, that 
is, the variable interval between sunrise and sunset, was always divided 
into 12 hours; therefore the day continually differed in length. By 
changing the aperture at bottom of the conical vessel, the clepsydra 
was regulated and made to keep pace with the variable hours. 

Sundial Time. — The time indicated by a sundial is 
apparent solar time, and no ordinary clock can follow it, 
except by accident. Previously to the nineteenth century, 
however, the attempt was made to construct clocks with 
such compensating devices that they would gain or lose, 
as referred to the stars, just as the sun does. But varia- 
tions in the sun's apparent motion are so complex that 
fine machinery necessary to follow the sun with precision 
could scarcely be made, even at the present day. Certainly 
its construction was impossible a century ago. 

Early in the 19th century apparent-time clocks were generally aban- 
doned, although in Paris they were in use as late as 181 5. Elaborate 
sundials are still occasionally met with, but their purpose is ornamental 
rather than useful. In a form of sundial easily constructed, a wire is 
adjusted parallel to the earth's axis, and its shadow falling upon a 
divided circular arc parallel to the equator tells the apparent time. 

To find True North quite Accurately. — As a preliminary to the 
arrangements for setting up any instrument in the meridian, or mount- 
ing it, as the technical expression is, true north must first be found with 
some accuracy. Select a window with a northern exposure, and a view 
down nearly to the north (sensible) horizon. From the top casing of 
the window, hang a long plumb-line, allowing the bob to swing freely 
in a basin of water. Secure it where it comes to rest, stretching the 
line taut. From a small table in the room hang another plumb-line in 
a similar manner, usino: fine, lio^ht-colored cord or cotton for the lines. 



ii6 



The Earth Turns on its Axis 



These arrangements should be made beforehand, as in the ilkistra- 
tion. The problem is to adjust the short line relatively to the long 
one, so that the vertical plane passing through the two plumb-lines 




Finding' True North without Clock or Telescope (from a Photograph b}'' Lovell) 

shall pass also through the pole star when crossing the meridian. This 
vertical plane will then itself be the meridian, and must therefore 
intersect the horizon in the true north and south points. But we have 
seen that the pole star, not being exactly at the north pole, describes 
a very small circle of the celestial sphere once every 24 sidereal hours ; 
therefore it must cross the meridian twice during that period. The 
intervals between these crossings will be nearly 12 ordinary hours. It 
is not at all necessary to know the exact local or ordinary time when 



A Rudimentary Trarisit Instrume^it 1 1 7 

the pole star is at the meridian ; but Polaris always comes into this 
position whenever Mizar (Zeta Ursae Majoris, the middle star in the 
handle of the Dipper) is also on the meridian. So it is only requisite 
to watch closely for the time when the long plumb-line passes through 
both these stars ; then, placing the eye near the floor, to move the 
table carefully until the short plumb-line hangs in the same plane with 
the long line and both stars. Be sure that the short plumb-Hne hangs 
perfectly free and still. A candle placed behind the observers head 
will show both lines, and at the same time not obscure the stars. Then 
by two permanent marks in the plane of the plumb-lines^ establish the 
meridian for convenient use. In line with Mizar and Polaris, and 
about as far on the opposite side of the pole, there chances to be 
another star, Delta Cassiopeiae, which, therefore, can be used in the 
same way as Mizar itself. Through nearly the entire year, either one 
or the other of these stars is available for finding true north, without 
any reference whatever to the clock. 

Times when Mizar and Delta Cassiopeiae are on the lower Merid- 
ian. — Begin watching before the lowxr star comes to the meridian. 
It will then appear to the left of the long plumb-line hanging through 
Polaris. Here is a table showing when to begin to watch : — 

For 8 Cassiopeia 



Dec. 


20 


7 A.M. 


Jan. 


20 


5 A.M. 


Feb. 


20 


3 A.M. 


Mar. 


20 


I A.M. 


Apr. 


20 


II P.M. 


May 


20 


9 P.M. 


June 


20 


7 P.M. 



For Mizar 


July 


20 


5 A.M. 


Aug. 


20 


3 A.M. 


Sept. 


20 


I A.M. 


Oct. 


20 


II P.M. 


Nov. 


20 


9 P.M. 


Dec. 


20 


7 P.M. 


Jan. 


20 


5 P.M. 



Both stars come about four minutes earlier every day. just as the 
south star did. During a part of June and July this method cannot be 
used, because it is strong twilight or daylight when Mizar and Delta 
Cassiopeiae are crossing the meridian. If repeated on a subsequent 
night, this method of establishing the local meridian wdll be found 
sufficiently accurate for mounting any astronomical instrument. Its 
adjusting screws will then bring it into closer range, w^hen the telescope 
can be brought into service to show the amount of deviation. If no 
telescope is available, a transit instrument may be made of a few com- 
mon materials, and the local time found by it approximately. 

A Rudimentary Transit Instrument. — The methods astronomers 
use in finding accurate time will be sketched in outline in Chapter ix. 
We here describe a method of getting the time within a few seconds by 



ii8 The Earth Turns on its Axis 

an observation of the sun. In the open air, or in a south window 
with a clear meridian from the south nearly up to the zenith, hang 
tw^o fine plumb-lines accurately in the meridian by the method just 
given. In line with them, firmly attach a strong box (about i8 inches 
square) to the window casing, as show^n in the illustration ; or better, 
to the east or west side of a building. By sighting along the plumb- 
lines, run a pencil mark round the outside of the box, to indicate the 



Observing the Time of Apparent Noon with the Eox-transit 

meridian roughly. Bore two f -inch holes in this mark, at points A and 
B. Also bore a third in the same plane near the middle of the upper 
face of the box. Over this lay a strip of sheet lead or tin, with a smooth 
pin hole through it, tacking it carefully so that the pin hole shall be in the 
plane of both plumb-lines. By sighting past these lines and through 
the holes A and B^ draw a fine straight pencil mark on the inside of the 
low^er face of the box, as shown, exactly in the plane of .the plumb-lines. 
If the box is exposed to the weather, this transit line may be scratched 
on a strip of tin, which may then be tacked in position by sighting 
through the holes A and B. 

If star transits are to be observ^ed in the open, a different arrange- 
ment of the meridian plane is necessary. Connect together the tw^o 
ends of a fine brass or copper wire about 20 feet long ; pass it over tw^o 
Doints in the meridian about 6 feet apart (north one perhaps two feet 



How Observatory Time is Foitnd 119 

above the south one) ; hook a heavy weight on the wire underneath, 
and when it stops swinging, fasten the double wire firmly. Bright 
stars at all meridian altitudes can be observed to cross this ^triangle 
transit,' with an error of only a few seconds. Comparison with a list 
of their right ascensions will then give the sidereal time. 

Observing the Sun's Transit. — Just before noon, a small round spot 
of light will be seen to the west of the inside mark. It is an image of 
the sun itself, about -^^ inch in diameter ; and it will be pretty sharply 
defined if the pin hole is smooth and round. The extreme positions of 
the image at the solstices are shown in the illustration. Watch the 
image as it slowly creeps toward the transit line ; observe the time 
with a watch when its edge first touches the line : there w^ill be an un- 
certainty of perhaps five seconds. Rather more than a minute later the 
image will be bisected by the hne ; observe this time also, likewise ob- 
serve the time when the following edge or limb of the sun becomes tan- 
gent to the line. Take the average of the three ; add or subtract the 
equation of time, as given in the table on page 113. The result will be 
local mean time, within a small fraction of a minute, provided the 
plumb-lines have been delicately adjusted in the meridian, and the geo- 
metric constructions of the transit box have been carefully made. A 
farther and constant correction will be required when the watch keeps 
standard time : if the place of observation is west of the standard me- 
ridian, add the amount of this difference of longitude in time ; if to the 
east of it, subtract this difference. 

Calculating the Sun's Transit. — On the 5th of February, 1897, at 
Amherst, Massachusetts (2° 28' 50'' = 9 m. 55 s. east of the standard 
meridian), the following times of transit were observed with the watch : — 

h. m. s. 

First limb of O tangent, 12 24 8 

Sun bisected, 12 25 25 

Second limb of O tangent, 12 26 33 

Mean, 12 25 22=watch time of apparent noon. 

Because sun is slow, subtract 14 16— equation of time. 

Difference, 12 11 6 = \vatch time of Amherst mean noon. 

Subtract for longitude, 9 55 = east of Eastern Standard meridian. 

Difference, 12 i ii=\vatch time of noon at standard meridian. 

12 o o 



Difference, i 11 = watch fast of standard time. 

How Observatory Time is found. — Recall the method 
of counting right ascensions of the heavenly bodies — 
eastward along the celestial equator from the vernal equi- 
nox to the hour circle of the body, counting from o h. round 



1 20 The Earth Turns on its Axis 

to 24 h. Sidereal time, as has just been shown, elapses in 
precisely the same way — from o h. o m. o s. when the ver- 
nal equinox is crossing the meridian, round to 24 h. o m. o s., 
when it is next on the meridian. Clearly, then, any star is 
on the meridian when the sidereal time is equal to its right 
ascension. But the right ascensions of all the brighter stars 
have been determined by the labor of astronomers in the 
past, and are set down in the Ephemeris and in star cata- 
logues. Also the same is given for sun, moon, and planets. 
Therefore, in practice, it is the converse of this relation 
which concerns us in the problem of finding the time by 
observing the transit of a heavenly body. Simply observe 
the time of its transit by the sidereal clock : if this time is 
the same as the body's right ascension, the clock has no 
error. If, as nearly always happens, the time of transit 
differs from the right ascension, this difference is the cor- 
rection of the clock ; that is, the amount by which it is fast 
or slow. Once the correction of the sidereal clock is 
found, the error of any other timepiece is ascertained 
from comparison with it. In observatories the mean solar 
time is rarely found by direct observation ; but it is cus- 
tomary to compare the mean-time clock with the sidereal 
clock, and then calculate the corresponding mean time by 
using the ' sidereal time of mean noon.' « 

Relation between Sidereal and Solar Time. — This rela- 
tion has been found by astronomers with the utmost pre- 
cision, and the quantities concerned in it are constantly used 
by them in ascertaining accurate time. The true relation 
is this : First, find how far the fictitious sun travels east- 
ward in one day. As it goes all the way round the celes- 
tial equator (360°) in one year, or 365^^ days, evidently in 
one day it travels nearly a whole degree (59' 8^^33, ac- 
curately). This angle, as we shall see in the next chapter, 
is nearly twice the apparent breadth of the sun. Now dur- 



Tlie Sidereal Time of Mean Noon 121 



ing a sidereal day an arc of 360°, 

or the entire equator of the heavens, 

passes the meridian of any given 

place. Therefore in a mean solar 

day, an arc of the equator equal to 

nearly 361° (accurately 360° 59' 8^^33) 

must pass the same meridian. From 

this relation we can calculate by 

simple proportion that 

24 mean solar hours 

= 24 h. 4m. sidereal time 

(accurately, 24 h. 3 m. 56.555 s.), 
and 24 sidereal hours 

= 23 h. 56 m. mean solar time 
(accurately, 23 h. 56 m. 4.091 s.). 

But we saw that the sidereal day of 
24 sidereal hours is the true period 
of rotation on its axis. One must, 
therefore, guard against saying that 
the period of the earth's rotation on 
its axis is 24 hours, unless specifying 
that sidereal hours are meant. By 
the term Jioiu^ as ordinarily used 
without qualification, the mean solar 
hour is understood. So that the 
true period in which the earth turns 
once on its axis is, not 24 hours, but 
23 h. 56 m. 4.09 s. 

The Sidereal Time of Mean Noon. 
— At every working observatory are 
two clocks, the one keeping sidereal 
time, the other mean solar time. Let 
us imagine both regulated to run 
perfectly. About the 20th March, 
at mean noon, when the fictitious 














122 



The Earth Turns on its Axis 



sun is crossing the equator, start both clocks from o hours, 
o minutes, o seconds, indicated by both dials. At the 
next mean noon, the mean-time clock will have come 
round to o h. o m. os. again, marking the beginning of 
a new astronomical day ; but the sidereal clock will 
indicate at the same instant oh. 3m. 56.55 s., because it 
has gained this difference during the 24 hours. At mean 
noon the next following day the sidereal clock will indi- 
cate o h. 7 m. 53. 1 1 s. ; and so on, perpetually gaining nearly 
4 m. every day. The figure just given makes this relation 
plain for a complete cycle of a year. The time, then, 

Table for finding the Sidereal Time of Mean Noon 



To THE Mean 


Time 


Add the 
ING Qu 


FOLLOW- 


To the Mean 


Time 


Add the 
ing Qu 


Follovv- 


















h. 


m. 






h. 


m. 


January . 




18 


45 


July . . . 




6 


40 






19 


40 






7 


35 


February . 




20 


45 


August . 




8 


40 






21 


40 






9 


40 


March . . 




22 


40 


September . 




10 


45 






23 


35 






II 


40 


April . . 







40 


October 




12 


45 






I 


35 






13 


40 


May 




2 


40 


November . 




14 


45 






3 


35 






15 


40 


June . 




4 


40 


December . 




16 


45 






5 


40 






17 


40 


July . . 




6 


40 


January . . 




18 


45 



shown (at each mean noon) by a sidereal clock perfectly 
adjusted, is called the ' sidereal time of mean noon.' * But 

* An approximate value is easily found by the above table ; if the given 
day is not the ist or the 15th, find the proper additive quantity by applying 4 
minutes for each day before or after the nearest day given in the table. 



Ascertaining Longitude 123 

as no clock can be made to carry on the time with absolute 
accuracy, these times are, in practice, not taken from a 
clock, but they are calculated and published in the Epliein- 
eris^ a set of astronomical tables issued by the Govern- 
ment two or three years in advance. As the sidereal times 
of all the mean noons through the year are absolutely 
accurate for all places on the prime meridian, they can be 
adapted to any place by simply applying a constant cor- 
rection dependent on its longitude. Clearly it is necessary 
to know the sidereal time of mean noon, if we desire to 
compare mean time with sidereal time at any instant ; and 
this calculation of one kind of time from the other is the 
most frequent problem of the practical astronomer. It can 
be made in a minute or two, and is accurate to the ^-^ part 
of a second. 

Ascertaining Longitude. — Longitude is angular distance 
measured on the earth's equator from a prime meridian to 
the meridian of the place. In England the prime meridian 
passes through the Royal Observatory at Greenwich, the 
prime meridian of France passes through the Paris Ob- 
servatory, and the prime meridian of the United States 
passes through the Observatory at Washington. Longitude 
is given in either arc or time. As the earth by turning 
round uniformly on its axis affords our measure of time, 
the meridians of the globe must pass uniformly underneath 
the stars ; so that finding the longitude of a place is the 
same thing as finding how much its local time is fast or 
slow of the local time of the prime meridian. 

Transit instruments are mounted and carefully adjusted at the two 
places whose difference of longitude is sought. By a series of observa- 
tions (usually of transits of stars), local sidereal time at each place 
is ascertained. Then time at both stations is automatically com- 
pared by means of the electric telegraph, and the difference of their 
times is the difference of their longitudes, expressed in time. The place 
at which the time is faster is the farther east. If there is no telegraph 



124 The Earth Turns on its Axis 

line or cable connecting the two stations, indirect and much less accu- 
rate methods of comparing their local times must be resorted to. So 
precise is the telegraphic method that the distance of Washington from 
Greenwich is known w^ith an error probably not exceeding 300 feet on 
the surface of the globe ; and where only land lines are employed, the 
distance of one place from another may be found even more accurately. 
Usually the time will be determined and signals exchanged on a series 
of six or eight nights ; and the entire operation of finding the longitude 
is called a longitude campaign. 

Standard Time. — Formerly, in traveling even a few 
miles, one was subjected to the annoyance of changing 
one's watch to the local time of the place visited. The 
actual difference between Boston and New York is 12 
minutes — between New York and Washington 12 min- 
utes ; and until within a few years each place kept only its 
own local time. But it was decided to establish a standard 
of time by which railroad trains should run and all ordinary 
affairs be regulated; and in November of 1883 this plan 
was adopted by the country at large, and time signals from 
Washington are now distributed throughout the United 
States every day at noon. The whole country is divided 
into four sections, or meridian belts, approximately 15 
degrees of longitude in width, so that each varies from 
those adjacent to it by exactly an hour. The time in the 
whole ' Eastern ' section is that of the 75th meridian from 
Greenwich, making it five hours slower than Greenwich 
time. This standard meridian coincides almost exactly 
with the local time of Utica and Philadelphia, and extends 
to Buffalo. Beyond that, watches are set one hour earlier, 
and the ^Central' section begins, just six hours slower 
than Greenwich time, employing 90th meridian time, which 
is almost exactly that of actual time at Saint Louis. 
This division extends to the center of Dakota, and in- 
cludes Texas. ' Mountain' or 105th meridian time is yet 
another hour earlier, seven hours slower than Greenwich, 



Sta7idard Time in Foreign CotuihHes 125 

and is nearly Denver local time. It extends to Ogden, 
Utah; and the * Pacific ' section, using 120th meridian 
time, is eight hours behind Greenwich, and ten minutes 
faster than local time at San Francisco. 

This simplifies all horological matters greatly, especially the run- 
ning of trains on the great railroads. While theoietically equal, these 
divisions are by no means so in reality, because variation is made from 
the straight line, in order to run each railroad system through on the 
same time, or make the change at great junctions. The cities just at 
the changing points may use either, and they make their own choice, 
Buffalo, for instance, choosing Eastern time, though Central would 
have been equally appropriate ; and Ogden choosing Mountain instead 
of Pacific. Wherever standard time is kept, the minute and second 
hands of all timepieces are the same. Only the hours differ. In 
journeying from one meridian belt into the next, it is only necessary to 
change one's watch by an entire hour, setting it ahead an hour if 
traveling eastward, and turning it back an hour when journeying west. 
In this country, accurate time is distributed by time balls, dropped 
at Boston, New York, Washington, and elsewhere, and by self-winding 
clocks controlled through the circuits of the Western Union Telegraph 
Company. The New York time ball is illustrated on page 9. 

Standard Time in Foreign Countries. — Within very re- 
cent years, the adoption of standard time has become 
nearly universal among the leading governments of the 
world. Almost without exception, the standard merid- 
ians adopted are a whole number of hours from the 
prime meridian of Greenwich, and local time in different 
parts of the world, corresponding to Greenwich noon, is 
shown in the Mercator map (page 127). In a few in- 
stances, where a country lies almost wholly between two 
such meridians, its accepted standard of time is referred 
to the half-hour meridian between the two. In some 
European cities, particularly London and Paris, accurate 
time is distributed automatically from a standard clock at 
a central station, or observatory. The more important 
foreign countries where standard time is used, with their 
adopted standards, are as follows : — 



126 The Earth Turns 07i its Axis 

Standard Time in Foreign Countries 



Country 


Standard 

Meridian 

East of 

Greenwich 


Time 

Fast of 

Greenwich 


Country 


Standard 

Meridian 

East of 

Greenwich 


Time 

Fast of 

Greenwich 






h. m. 


s. 






h. 


m. 


Great Britain 


o" o' 








Cape Colony . 


22"* 30' 


I 


30 


France 


2 20 


9 


21 


Natal . . . 


30 


2 





Germany . 


15 


I 





West Aus- 








Italy . . . 


15 


I 





tralia 


120 


8 





Austria 


15 







Japan . 


135 


9 





Denmark . . 


15 


I 





S. Australia . 


^3S 


9 





Norway . 


15 


I 





Victoria . 


150 


10 





Sweden . 


15 


I 





Queensland . 


150 


10 





Belgium . . 


15 


I 





Tasmania . . 


150 


10 





Holland . . 


15 


I 





New Zealand . 


172 30 


II 


30 



Travelers in these countries, therefore, have only to set their watches 
according to these differences of time. In general, it is evident that 
only the hour hand needs changing, the minutes and seconds remain- 
ing the same as in England or America. The second and minute 
hands of all clocks and watches keeping exact standard time in the 
United States, Japan, Australia, and nearly the whole of Europe read 
the same : their hour hands alone differ. 



Uniformity of the Earth's Rotation. — It is now clear 
that the turning of the earth on its axis is of very great 
service, not only to the astronomer in making his investi- 
gations, but to mankind in general, as affording a very 
convenient means of measuring time. Everything is based- 
on the absolute uniformity of this rotation. Reliance is — 
indeed, must be — implicit. Yet it is possible to test this 
important element by comparing it with known move- 
ments of other bodies in the sky, particularly the moon, 
the earth, and the planet Mercury round the sun. The 
deviations, if any, are nearly inappreciable ; and the slight 
slackening of its rotation at one period seems to be coun- 




127 



128 



The Earth Turns 07t its Axis 



terbalanced by an equal acceleration at another. So that 
if irregularities actually do exist, they probably cancel each 
other in the long run, and leave the day invariable in 
length. Uniformity of the earth's rotation has been criti- 
cally investigated 
by Newcomb, and 
no change in 
the length of the 
day as great as 

ToVo ^^ ^ second 
in a thousand years 
could escape de- 
tection. 

Precession of the 
Equinoxes, — The 
equinoxes have a 
slow motion, partly 
produced by the 
earth's turning on 
its axis. The eclip- 
tic remains invari- 
able in position, 
and equator and 
ecliptic are always 
inclined to each 
other at practically 
the same angle ; but this motion of the equinoxes is a glid- 
ing of equator round ecliptic, and is called precession. The 
equinoxes travel westward about 50^^^ annually ; so that 
in rather less than 13,000 years, the vernal equinox will 
have slipped round to the position formerly occupied by 
the autumnal equinox. In 25,900 years precession com- 
pletes an entire cycle, both equinoxes returning to their 
position at the beginning of it. 




A Model to illustrate Precession 



Effects of Precession 



129 



Precession is so important in astronomy that the phenomenon 
should be perfectly understood. Over a tub nearly filled with water, 
suspend a barrel hoop by three cords, two of which, equal in length, 
are attached to the hoop at the extremities of a diameter.. The third 
cord, a few inches shorter than the other two, is tied to the hoop mid- 
way between them. Fasten three weights of about one pound each at 
the same points. Gather the three cords together into one. at a few 
feet above the hoop, and tie them to a right-hand-twisted cord a few 
feet long. To represent the earth, with axis perpendicular to the hoop, 
secure any common spherical object in the center of the hoop, by a 
crosspiece nailed to hoop as indicated. Suspend the whole by the 
twisted cord as shown in the picture, lowering it until the hoop is im- 
mersed to the knots of the two short cords. These represent the 
equinoxes, the hoop itself the celestial equator, and the surface of w^ater 
in the tub stands for plane of ecliptic. i\djust the shorter cord so that 
the hoop shall be tilted to the water about 23 p. Now release the hoop, 
and it will twirl round clockwise ; the motion of the two opposite knots 
will correspond to precession of the equinoxes, and represent the long 
period of precession, 25,900 years in duration. This motion round the 
signs of the zodiac (in the direction Aries, Pisces, Aquarius), is repre- 
sented by the arrow in the illustration on page 65. Pole of ecHptic is 
E^ and round it as a center moves P, the earth's pole, in a small circle, 
PpSV, 47° in diameter. 



Effects of Precession. — On account of precession, right 
ascensions and declinations of stars (being referred to the 
equator as a fundamental plane) are continually changing. 
Precession of 
the equinoxes 
was first found 
out by Hippar- 
chus (b.c. 150). 
About B.C. 2200, 
the vernal equi- 
nox was near 
the Pleiades as 
in the adjacent figure. Since that time it has traveled 
back, or westward, about 60°, through Aries, until now it is 
in the western part of Pisces, as on the following page. So 
todd's astron. — 9 




Vernal Ecuino" 



C. 22C0> 



I30 



The Earth Turns on its Axis 




the signs of the zodiac do not now correspond with con- 
stellations which bear the same names, as they did in the 
time of Hipparchus ; and the two systems are becoming 
more and more separated as time elapses. Because the 
direction of earth's axis in space is changing, the north 

celestial pole is slowly 
moving among the 
stars, in a small circle 
whose center is the 
north pole of the eclip- 
tic; and it will complete 
its circle in the period of 

Vernal Equinox now in Pisces prCCCSSion itSClf. That 

important star Polaris, our present north star because now 
so near the intersection of earth's axis prolonged north- 
ward to the sky, has not always been the pole star in the 
past, nor will it always be in the future. If circumpolar 
stars w^ere photographed in trails, as on page 33, at inter- 
vals of a few hundred years, the curvature of arcs traversed, 
by a given star w^ould change from time to time. About 
200 years hence, the true north pole wall be slightly 
nearer Polaris than it now is, and afterward the pole will 
retreat from it. About B.C. 3000, Alpha Draconis was the 
pole star; and 12,000 years hence, Vega (Alpha Lyrae) 
will enjoy that distinction. Regarding positions of stars 
as referred to the ecliptic system, their latitudes cannot 
change, because ecliptic itself is fixed. But longitudes of 
stars must change, much as right ascensions do, because 
counted from the moving vernal equinox. Besides rotation 
about its axis, the earth has another motion of prime 
importance, which we shall now discuss. 



CHAPTER VII 

THE EARTH REVOLVES ROUND THE SUN 

HITHERTO explanation has been given only of that 
apparent motion of the heavenly bodies which is 
common to all — a rising in the east, crossing the 
meridian, and setting in the west. Although this motion 
was reo;arded as real in the ancient svstems of astronomv, 
we have seen that it is satisfactorily explained as a purely 
apparent motion, due to the simple turning round of the 
earth on its axis once each day. Now we shall consider 
an entirely different class of celestial motions ; we know 
that they take place because our observations show that 
none of the bodies which are tributarv to the sun are 
stationary in the sky. This point will be fully dwelt upon 
in a subsequent chapter on the planets. On the contrary, 
all seem to be in motion among the stars ; at one time for- 
ward or eastward, and at another backward or toward the 
west. All through the period of the infancy of astronomy, 
a fundamental mistake was made ; too great importance 
was attached to the earth, because men dwell upon it, and 
it seemed natural to regard it as the center about which 
the universe wheeled. Centuries of investigation were 
required to correct this blunder ; and true relations of 
the celestial mechanism could be understood only when 
real motions had been thought out and put in place of 
apparent ones. The earth was then forced to shrink into 
its proper and insignificant role, as a planet of only modest 

131 



132 The Earth Revolves Round the Sun 

proportions, itself obedient in motion to the overpowering 
attraction of the sun. 

The Sun's Apparent Annual Motion. — First, let us again 
observe the sun's seeming motion toward the east. Soon 
after dark, the first clear night, observe what stars are due 
south and well up on the meridian. A week later, but at 
the same time of the evening, look for the same stars ; 
they will be found several degrees west of the meridian. 
Why the change } These stars, and all the others with 
them, seem to have moved westward toward the sun ; or 
what is the same thing, the sun must have moved eastward 
toward these stars. But while this appears to be a motion 
of the sun, we shall soon see that it is really a motion of 
the earth round the sun. If our globe had no atmosphere, 
the stars would be visible in the daytime, even close be- 
side the sun ; and it would be possible, directly and with- 
out any instruments, to see him approach and pass by 
certain stars near his path from day to day. A few obser- 
vations would show that the sun seems to move eastward 
about twice his own breadth, that is 1°, every day. His 
path among the stars would be found to be practically the 
same from year to year. This annual path of the sun 
among the stars is called the ecliptic, and invariability 
of position has led to its adoption by astronomers from 
the earliest times, as a plane of reference. Its utility as 
such has already been considered in Chapters 11 and iii ; it 
is the fundamental plane of the ecliptic system. 

Sun's Apparent Motion really the Earth's Motion. — 
What causes that apparent motion of the sun just described '^. 

Select a room as large as possible in which there is a tall lamp. 
Place this in the center of the room, and walk around it counter-clock- 
wise, facing the lamp all the time ; notice how it seems to move round 
among and pass by the objects on the wall. It appears to travel with 
the same angular speed that you do. and in the same direction. Now 
imagine yourself the earth, the lamp to be the sun, and the objects on 



Ear i /is Orbit the Ecliptic Plane 133 

the wall the fixed stars. The horizontal plane through the lamp and 
the eye will represent the ecliptic ; one complete journey round the 
lamp will correspond to a year. 

A simple experiment of this character will convey a 
clear idea of the true explanation of the sun's apparent 
motion : that great luminary is himself stationary at the 
center of a family or system of planets, of which our earth 
is merely one ; and our globe by traveling round the sun 
once each year causes him to appear to move. If, however, 
it is not clear how the earth's motion is the true cause of 
the sun's seeming to describe his annual arc round the 
ecliptic, put yourself in place of the lamp and have some 
one carry the lamp round you, counter-clockwise. Mean- 
while keep your eye constantly upon the lamp, and observe 
that it seems to move round on the wall in just the same 
direction and at the same speed as when the lamp was sta- 
tionary and you walked around it. 

Earth's Orbit the Ecliptic Plane. — The real path which 
one body describes round another in space is called its 
orbit. The path our globe travels round the sun each year 
is called the earth's orbit. We cannot see the stars close 
to the sun, nor observe his position among them each day ; 
but practically the same thing is done by means of instru- 
ments in government observatories. While these observa- 
tions of the sun's position are going on from the earth, 
imagine a similar observatory on the sun, at which the 
earth's positions among the stars are recorded at the same 
times. Every earth observation of the sun w411 differ from 
its corresponding sun observation of the earth by exactly 
180°. But the earth observations of the sun are all in- 
cluded in that great circle of the sky called the ecliptic, 
therefore all the sun-observed positions of the earth (that 
is, the earth's own positions in space) must also be in the 
ecliptic. They are therefore included in a plane. 



134 ^/^^ Earth Revolves Rozind the Sun 



Which Way is the Earth traveling ? — In attempting to 
pass from a conception of the earth at rest as it seems, to 
the earth moving round the sun as it really 
is, no help can be greater than the frequent 
pointing toward the direction in which the 
earth is actually traveling. The gradual 
and regular variation of this direction with 
the hours of day and night, and its rela- 
tion to fixed lines in a 
Mt%- room or building, will 
'^ soon mipress nrmly 
the mind the 
the earth's annual motion 
round the sun. 




upon 



great truth of 



6 A.M. — Earth traveling" up 



Extend the arms at right angles 
to each other as in the illustration. 
Swing round until the left arm is 
pointed toward the sun, whether 
above or below the horizon. This 
arm will then be in the plane 
of the ecliptic. Still keep- 
ing the arms at right angles, bring 
the right arm as nearly as ma\' be 
into the plane of the ecliptic at the 
time. This may be done as al- 
ready indicated on page 67. The right arm 
will then be pointing in the direction in which 
the earth is journeying in space. The right arm 
holding the ball and arrow is always pointing in 
the direction of earth's motion through space, 
relatively to the local horizon in the latter part 
of September : 

(i) at 6 A.M.. upward toward a point about 
20^ south of the zenith : 

(2) at noon, toward the northwest, at an alti- 
tude of about 10' : 

(3) at 6 p M.. downward to a point about 20'^ 
below^ the north horizon ; 

(4) at midnight, toward the northeast at an altitude of about 10 







1 2 Noon — Earm traveling 
Westward 



Direction of Eartlis Motion 



135 




6 P.M. — Earth traveling 
Downward 



It is apparent that the direction of the earth's motion is simply the 
direction of a point whose celestial longitude is 90' less than that of 
the sun. This moving point 
is often called the earth's 
goal, or the apex of the 
earth's way. ^\^^ 

Change in Absolute 
Direction of Earth's Motion. — In an 

early chapter was explained how east 

and west, north and south at a given 

place are always changing with the 

earth's turning on its axis, and that it is 

necessary to think of these directions as 

curving round with the surface of the 

earth. We saw, too, that the same rela- 
tions exist with reference to the cardinal 

points of the celestial sphere, so that 

east, for example, in one part of the heavens, is the same 

absolute direction as west on the opposite part of the 

celestial sphere. In precisely 
the same way we have now to 
D=^ think of the absolute direction 
\ of earth's movement round the 
sun as continually changing in 
space. If at one moment there is a star 
exactly toward which the earth is trav- 
eling, three months before that time and 
three months afterward we shall be going 
at right angles to a line from the sun to 
that star ; and six months from the given 
time we shall be traveling exactly away 
from it. In the chapter relating to the 
stars it will be shown how this motion of 

12 Midnight — Earth , , . ^ n i j 

traveling Eastward the earth m spacc cau actually be de- 




136 The. Earth Revolves Round the Sun 

monstrated by a delicate observation with an instrument 
called the spectroscope. 

Earth's Orbit an Ellipse. — The angle which the sun 
seems to fill, as seen from the earth, is called the sun's 
apparent diameter. Measures of this angle, made at 
intervals of a fcAv days throughout the year, are found to 
differ very materially. It is not reasonable to suppose 
that the size of the sun itself varies in this manner. 
What, then, is the explanation } Obviously the sun's dis- 
tance from us, or, what is the same thing, our distance 
from him, is a variable quantity. The earth's orbit, then, 
cannot be a circle, unless the sun is out of its center. But 
the observations themselves, if carefully made, will show 
the true shape of the orbit. It is not necessary to know 
what the real distance of the sun is, because we are here 
concerned with relative distance merely, nor need the ob- 
servations be made at equal intervals. In an early chapter 
we saw that the apparent size of a body grows less as its 
distance becomes greater. Apply this principle to the 
measures of the sun. 

Plot the observations by drawing radiallines at angles corresponding 
to various directions in tlie ecliptic ^yhen observations of the sun's 
breadth vrere made. Cut off the radial lines at distances from the 
radial point proportional to the observed diameters, and then draw a 
regular curve through the ends of the radial lines. On measuring this 
curve, it is found that it deviates only slightly from a circle, but that it 
is really an ellipse, one of whose foci is the radial point. Earth's orbit 
round the sun, then, is an ellipse, with the sun at one focus. 

The Ellipse. — The ellipse is a closed plane curve, the 
sum of the distances from every point of which, measured 
to two points within the curve, is a constant quantity. This 
constant fixes size of the ellipse, and is equal to its longer 
axis, or major axis (figure opposite). At right angles to 
the major axis, and through its center is the minor axis. 
The two determining points are called foci, and both of 



Limits of tJie Ellipse 



^11 




Ellipse, Foci, Axes, and Radii Vectores 



them are situated in the major axis, at equal distances 

from the center of the elHpse. Divide the distance from 

the center to either focus by the half of the major axis, 

and the quotient is called 

the eccentricity. This 

quantity fixes the form 

of the ellipse. If the 

foci are quite near the 

center, the eccentricity 

becomes very small, and 

the curve approaches the 

circle in form. If the 

center and both foci are 

merged in a single point, evidently the ellipse becomes an 

actual circle. This is called one limit of the ellipse. But 

if the foci recede from the center and approach very near 

the ends of the major axis, then the corresponding ellipse 

is exceedingly flattened; and its limit in this direction 

becomes a straight line. 

Limits of the Ellipse. — These two limits are easy to 
illustrate, practically, by looking at a circular disk {a) 
perpendicularly, and {b) edge on. In tilting it 90° from 
one position to the other, the ellipse passes through all 
possible degrees of eccentricity. The orbits of the heav- 
enly bodies embrace a wide range of eccentricity. Some of 
them are almost perfectly circular, and others very eccen- 
tric. In drawing figures of the earth's orbit, the flatten- 
ing is necessarily much exaggerated, and this fact should 
always be kept in mind. The eccentricity of the earth's 
orbit is about ^-^ ; that is, the sun's distance from the 
center of the orbit is only ^-^ part of the semi-major axis. 
If it is desired to represent the earth's orbit in true pro- 
portions on any ordinary scale, the usual way is to draw 
it perfectly circular, and then set the focus at one side of 



138 The Earth Revolves Round the Sit 



ji 



the center, and distant from it by -^-^ the radius. If the 
center is obliterated, a well-practiced eye is required to 
detect the displacement of the focus from the center. And 
as we shall see, many of the celestial orbits are even more- 
nearly circular than ours. 

How to draw an Ellipse. — The definition of an ellipse suggests at 
once a practical method of drawing it. Lay down the major axis and 
the minor axis. From either extremity of the latter, with a radius equal 
to half the major axis, describe a circular arc cutting the major axis in 
two parts. These will be the foci. Tie together the ends of a piece of 
fine, non-elastic twine, so that the entire length of the loop shall be 

equal to the major axis added 
i^ to the distance between the 

^ foci. Set two pins in the foci, 

5 place the cord around them, 

and carry the marking point 
round the pins, holding the 
cord all the time taut. The 
point will then describe an 
ellipse with sufficient accuracy. 

Lines and Points in El- 
liptic Orbits. — The earth 
is one of the planets, and 
in treating of them the 
laws of their motion in 
elliptic orbits will be 
given. In a still later 
chapter the reason why 
they move in orbits of 
this character will be ex= 
plained. Here are de- 
fined such terms as are 




Earth's Orbit (Ellipticity much exag-gerated) 



necessary to understand in dealing with the earth. Only 
one of the foci of the orbit need be considered. In that one 
the primary body is always located. Any straight line 
drawn from the center of that body, as S, to any point of 



Eartlis Orbit in the Future 1 39 

the ellipse, as E, is called a radius vector. The longest 
radius vector is drawn to a point called aphelion ; the short- 
est radius vector, to perihelion. Together these two radii 
vectores make up the major axis of the orbit. Perihelion is 
often called an apsis ; aphelion also is called an apsis. A 
line of indefinite length drawn through them, or simply the 
major axis itself unextended, is called the line of apsides. 
Imagine the point where the line of apsides, on the peri- 
helion side, meets the celestial sphere to.be represented by 
a star. The longitude of that star, or its angular distance 
measured counter-clockwise from the first of Aries, is tech- 
nically called the longitude of perihelion. This is 100° 
in the case of the earth. The longitude of perihelion in- 
creases very slowly from year to year ; that is, the apsides 
travel eastward, or just opposite to the equinoxes. But, 
slow as the equinoxes move, the apsides travel only one 
fourth as fast. 

Earth's Orbit in the Future. — Not only does the hne 
of apsides revolve, but the obliquity of the ecliptic (page 
150) changes slightly, and even the eccentricity of the 
earth's orbit varies slowly from age to age. These facts 
were all known a century or more ago ; but with regard 
to the eccentricity, it was not known whether it might 
not tend to go on increasing for ages. Should it do so, 
the earth would be parched at every perihelion passage, 
and congealed on retreating to aphelion: it seemed among 
the possibilities that all life on our planet might thus be 
destined to come to an end, although remotely in the 
future. But in the latter part of the eighteenth century, 
a great French mathematician, La Grange, discovered 
that although the earth's orbit certainly becomes more and 
more eccentric for thousands of years, this process must 
finally stop, and it then begins to approach more and 
more nearly the circular form during the following period 



140 The Earth Revolves Round the Sun 



of thousands of years. At present it is near the average 
value, and will be decreasing for the next 24,000 years. 
He showed, too, that the obliquity of the ecliptic simply 
fluctuates through a narrow range on either side of an 
average value. These slight changes are technically 
called secular variations, because they consume very long 
periods of time in completing their cycle. The mean or 
average distance, and with it the time of revolution round 
the sun, alone remains invariable. As w^e know this 
period for the earth, and the eccentricity of its orbit 
together with the location of its perihelion point, by cal- 
culating forward or backward from a given place in the 
sky on a given date, we can find the position of the sun 
(and therefore of the earth in its orbit) with great accu- 
racy for any past or future time. 

Earth's Motion in Orbit not Uniform . — Refer back to 
the observations of the sun's diameter by which it was 
shown that our orbit round the sun is not a circle, but an 
ellipse. Had they been made at equal intervals of time, 
it would at once have been seen, on plotting them, that 

the angles through which 
the radius vector travels 
are not only unequal, but 
that they are largest at 
perihelion, and smallest at 
aphelion. By employing 
mathematical processes, 
it is easy to show from the 
observations of diameter, 
connected with the corresponding angles, that a definite 
law governs the motion of the earth in its orbit. Kepler 
was the first astronomer who discovered this fact, and 
from him it is called Kepler's law. It will seem remark- 
able until one apprehends the reason underlying it. The 




Radius Vector sweeps Equal Areas in 
Equal Times 



The Unit of Celestial Measurement 141 

law is simply this : The radius vector passes over equal 
areas in equal times. That the figure opposite may illus- 
trate this, an ellipse is drawn of much greater eccentricity 
than any real planetary orbit has. What the law asserts is 
this : Suppose that in a given time, say one month, the 
earth in different parts of its orbit moves over arcs equal 
to the arrows ; then the lengths of these arrows are so pro- 
portioned that their corresponding shaded areas are all 
equal to each other. And this relation holds true in all 
parts of the orbit, no matter what the interval of time. 

The Unit of Celestial Measurement. — By taking the 
average or mean of all the radii vectores, a line is found 
whose length is equal to half the major axis. This is 
called the mean distance. The mean distance of the 
center of the earth from the center of the sun we shall 
next find from the velocity of light. This distance is 
93,000,000 miles, and it is the unit of measurement uni- 
versally employed in the astronomy of the solar system. 
Consequently, it is often called distance tmity ; and as 
other distances are expressed in terms of it, they have 
only to be multiplied by 93,000,000, to express them in 
miles also. 

Trying to conceive of this inconceivable distance is worth the 
while. Illustrations sometimes help. Three are given : {a) If you had 
silver half dollars, one for every mile of distance from the earth to the 
sun, they would fill three ordinary freight cars. If laid edge to edge in 
a straight line, they would reach from Boston to Denver. (^) It has been 
found by experiment that the electric wave in ordinary wires travels as 
far as from New York to Japan and back in a single second (about 
16,000 miles). If you were to call up a friend in the sun by telephone, 
the cosmic line would be sure to prove more exasperating than terres- 
trial ones sometimes are ; for even if he were to respond at once, you 
would have to wait 3^^ hours, {c) Suppose that as soon as George 
Washington was born, he could have started for the sun on a fast 
express train, like the one illustrated on page 45, which can make long 
runs at the rate of 60 miles an hour. Suppose, too, that it had been 
keeping up this speed ever since, day and night, without stopping. A 



142 The Earth Revolves Roinid the Sim 



long, long time to travel continuously, but his body would still be on 
the road, for the train would not reach the sun till 1907. 

Finding the Velocity of Light by Experiment. — Light 
travels from one part of the universe to another with " 
inconceivable rapidity. Light is not a substance, because 
experiment proves that darkness can be produced by the 
addition of two portions of light. Such an experiment is 
not possible w4th substances. All luminous bodies have 
the powder of producing in the ether a species of wave 
motion. The ether is a material substance which fills all 
space and the interstices of all bodies. It is perfectly 
elastic and has no weight. As light travels by setting up 
very rapid vibrations of the particles of the ether, it is 
usually called the luminiferous ether. Different from the 
vibrations of the atmospheric particles in a sound wave, 

light waves travel by 
vibrations of the ether 
athwart the course of the 
ray. The velocity of wave 
transmission is called the 
velocity of light. It is not 
difficult to find by actual 
experiment. 




One method is illustrated by 

the figure. A ray of light is 

thrown into the instrument at 

Bs in the direction of the dotted 

line. It is reflected at C and 

goes out of the telescope A to 

a distant mirror, which reflects 

^ it directly back to the telescope 

Finding Velocity of Light again, and the observer catches 

the retui"n ray by placing the eye 

at D. In the field of the telescope are the teeth of a wheel E. through 

which outgoing and returning rays must pass. With the wheel at rest. 

the return rav is fully seen between the teeth of the wheel. Whirl the 



Size of the Eartlis Orbit 143 

wheel rapidly. While the direct ray is going out to the mirror and 
coming back to the wheel, a tooth will have moved partly over its own 
width, and will therefore partly shut off the ray, so that the star appears 
faint instead of light. Whirl the wheel faster, and the return ray be- 
comes invisible. Keep on increasing the velocity of the wheel, and the 
star again reappears gradually. And so on. iMore than twenty disap- 
pearances and reappearances can be observed. The speed of the wheel 
is known, because its revolutions are registered automatically by the 
driving apparatus (omitted in the figure) ; and the distance of the mir- 
ror from the wheel can be accurately measured, so that the velocity of 
light can be calculated. 

This and other similar experiments have often been 
repeated by Cornu, Michelson, Newcomb, and others, in 
Europe and America ; and the result of combining them 
all is that light waves, regardless of their color, travel 
186,300 miles in a second of time. 

Size of the Earth's Orbit. — Where matters pertaining 
to elementary explanation are simplified by so doing, it is 
evident that the earth's orbit may be regarded as a circle. 
From several hundred years' observation of the moons 
which travel round the planet Jupiter, it has been found 
that reflected sunlight by which we see them consumes 
998 seconds in traveling across a diameter of the earth's 
orbit (page 345). So that \ x 998 x 186,300 is the radius 
of that orbit, or the mean distance of the sun. This 
distance is 93,000,000 miles, just given. Earth is at 
perihelion about the ist of January each year, and on 
account of eccentricity of our orbit we are about 3,000,000 
miles nearer the sun on the ist of January than on the 
1st of July. Our globe travels all the way round this 
vast orbit, from perihelion back to perihelion again, in 
the course of a calendar year. Clearly, its motion must 
be very swift. Hold a penny between the fingers at a 
height of four feet. Suddenly let it drop: in just a half 
second it will reach the floor. So swiftly are we traveling 
in our orbit round the sun, that in this brief half second 



144 ^/^^ Earth Revolves Round tJie Su 



n 



we have sped onward 9^ miles. And in all other half 
seconds, whether day or night, through all the weeks and 
months of the year, this almost inconceivable speed is 
maintained. 

Earth's Deviation from a Straight Line in One Second. — 
As our distance from the sun is approximately 93,000,000 
miles, the circumference of our orbit round him (consid- 
ered as a circle) is 584,600,000 miles. But as we shall 

see in a later paragraph, the 
earth goes completely round 
the sun in one sidereal year, 
or 365 d. 6 h. 9 m. 9 s. ; there- 
fore in one second our globe 
travels through space i8j 
miles. In that short interval, 
how far does our path bend 
awa}^ from a straight line, or 
tangent to the orbit } Sup- 
pose that in one second of 
time, the earth w^ould move 
in a straight line from J/ 
to N, if the sun exerted no 
attraction upon us. Because 
of this attraction, however, we 
travel over the arc Mn. The length of this arc is 18^ 
miles, or about o'^04 as seen from the sun ; and as this 
angle is very small, the arc Mn may be regarded as a 
straight line, so that MnU \^ a right angle. Therefore 




Earth's Deviation in One Second 



MU\ Mn\ : Mn\ Mm 

But MU'v^ double our distance from the sun; therefore^ 
Mm is o. 119 inch, which is equal to Nn, or the distance 
the earth falls from a straight line in one second. So 
that we reach this very remarkable result : The curvature 



Solar and Sidereal Day 



145 



of our path round the sun is such that in going i Si- 
miles we deviate from a straight line by only ^ of an 
inch. 

Reason for the Difference between Solar and Sidereal 

Day. — The real reason why the sidereal day is shorter 
than the solar day can now be made clear. The figure is 
a help. If earth were not moving round the sun, but 
standing still in space, one sidereal day would be the time 
consumed by a point on the equator, A^ in going all the way 




Sidereal and Solar Day compared 



round in direction of the lower arrows, and returning to 
the point of starting. But while one sidereal day is elaps- 
ing, the earth is speeding eastward in its orbit, from OX.0 O' , 
Sun and star were both in the direction AS 'Bit the begin- 
ning; but after the earth has turned completely round, 
the star will be seen in the direction O' A^ which is par- 
allel to OA, because 00' is an indefinitely small part of 
the whole distance of the star. This marks one sidereal 

TODD'S ASTRON. — lO 



146 The Earth Revolves Round the Sun 

day. The sun, however, is in the direction O^ S\ and the 
solar day is not complete until the earth has turned round 
on its axis enough farther to bring A underneath 5. This 
requires nearly four minutes ; so the length of the solar 
day is 24 hours of solar time, while the sidereal day, or 
real period of the earth's rotation, equals 23 h. 56 m. 4.09 s. 
of solar time. Also in the ordinary year of 365^ solar 
days, there are 366^ sidereal days. 

Sun's Yearly Motion North and South. — You have found 
out the eastward motion of the sun among the stars from 
the fact that they are observed to be farther and farther 




Direction of Sun's Rays at Equinoxes and Solstices 

west at a given hour each night. You must next ascer- 
tain the nature of the sun's motion north and south. The 
most convenient way will be to observe where the noon 
shadow of the top of some pointed object falls. Begin 
at any time of the year; in autumn, for example. This 
shadow will grow longer and longer each day ; that is, the 
noonday sun is getting lower and lower down from the 
zenith toward the south. How low will it actually go .'^ 
And when is this epoch of greatest length of the shadow } 
Even the crudest observation shows that the noonday 



The Suns Yearly Motion North 147 

shadow will continue lengthening till the 20th of Decem- 
ber; but the daily increase of its length just before that 
date will be difficult to observe, it is so very slight. Then 
for a few days there will be no perceptible change ; in so 
far as motion north or south is concerned, the sun appears 
to stand still. As this circumstance was the origin of the 
name solstice, notice that it indicates both time and space : 
the winter solstice is the time when (or the point in the 
celestial sphere zvhere) the sun appears to ' stand still ' at 
its greatest declination south. The time is about the 20th 
of December. Not until after Christmas will it be possible 
to observe the sun moving north again ; and then, at first, 
by a very small amount each day. 

The Sun in Midwinter. — For the sake of comparison 
with other days in the year, let us photograph (at noon 
on a bright day near the winter solstice) some familiar 
object with a south exposure; for example, a small and 
slender tree, with its shadow (next page). Observe how 
much shorter tree is than shadow, because the sun culmi- 
nates low. So far north does the shadow of the tree fall 
that a part of it actually reached the house where the camera 
stood. Verify the northeast-by-east direction of the sunset 
shadow of the tree ; and the corresponding direction (north- 
west-by-west) of its sunrise shadow, also ; for the sun will 
now rise at a more available hour than in midsummer. 
Notice, too, how sharply defined the shadow is, near the 
trunk of the tree ; and how ill-defined the shadows of the 
branches are. This is because the sun's light comes from 
a disk, not a point ; the shadows are penumbral, that is, 
not quite like dark shadows ; and they grow more and 
more hazy, the farther the surface upon which they fall. 

The Sun's Yearly Motion North. — Onward from the 
beginning of the year, continue to watch the sun's slow 
march northward. With each day its noontime shadow 



148 The Earth Revolves Round the Sun 



will grow shorter and shorter. Watch the point in the 
western horizon where the sun sets ; with each day this, 
too, is coming farther and farther north. Note the day 

when the sun sets ex- 
actly in the west ; this 
will be about the 20th 
of March. As the 
sun sets due west, 
evidently it must pre- 
viously have risen due 
east ; therefore the 
I great circle of its 

diurnal motion (which 
at this season is the 
equator) must be bi- 
sected by the horizon. 
Day and night, then, 
are of equal length. 
The vernal equinox is 
the time when (or the 
point where) the sun 
going northward 
crosses the celestial 
equator. 

The Sun in Mid- 
summer. — Now be- 
gin again the obser- 
vations of the noon- 
time shadow. Shorter 
and shorter it grows and perceptibly so each day. But it 
will be noticed that the difference from day to day is less 
than the daily increase of length six months before. That 
is simply because the shadows fall nearer the tree, and are 
measured more nearly at right angles to the sun's direction 




Midwinter Shadows Longest 



The Sun in Midsummer 



149 



than they were in the autumn and winter. The azimuth 
of its setting will increase. How many weeks will the 
length of the shadow continue to decrease } How short 
will it actually get 1 About the middle of June, it will be 
almost impossible to 
notice any further de- 
crease in the shad- 
ow's length, and on 
20th June we may 
again photograph 
the same tree. But 
how changed ! The 
short shadow of its 
trunk is all merged 
in the shadow of 
the foliage where it 
falls upon the lawn. 
Points of the compass 
alone are unchanged. 
Here again at mid- 
summer, the sun 
stands still, and there 
is a second solstice. 
Summer solstice is 
the time when (or 
the point on the celestial sphere where) the sun appears 
to * stand still ' at greatest declination north. Do not fail 
to notice the points of the compass. Alsa verify at mid- 
summer the indicated direction (southeast-by-east) in which 
the tree's shadow falls at sunset ; and near the beginning 
of the summer vacation it will be worth while to arise once 
at five o'clock in the morning, in order to verify also the 
southwest-by-west direction of the shadow just after sun- 
rise. By the latter part of June, the noontime shadow 




Midsummer Shadows Shortest 



150 The Earth Revolves Rou7td the Sun 

again begins to lengthen ; more and more rapidly with 
each day it lengthens until the equinox of autumn, when 
the cycle of one year of observation is complete. 

To observe the Inclination of Equator to Ecliptic. — As equator and 
ecliptic are both great circles, the sun goes as far north in summer as 
it goes south in winter. Half the extreme range is the angle of incli- 
nation of ecliptic to equator, and it is technically termed the obliquity 
of the ecliptic. Its value for 1900 is 23° 27' 8'^02, and it changes very 
slowly. A rough value is readily found for any year by making use of 
the latitude-box already described on page 82. At noon on the 20th, 
2 1st, and 22d of December, observe the readings on the arc where 
the sun's line falls. Be sure that the box remains undisturbed, or test 
the vertical arm of the quadrant by the plumb-line each day. Leave the 
box in position through the winter and spring, or set up the same box 
again in June, and again apply the plumb-line test. At noon on the 
20th, 2 1st, and 22d of June, observe the sun's reading as at the other 
solstice. Take the difference of readings as follows : — 

Reading of 22d December from 20th June ; 
2 1st December from 21st June ; 
20th December from 2 2d June. 

Then halve each of the three differences, and the results will be three 
values for the inclination of equator to ecliptic. Take the average of 
them for your hnal value. Thus in about six months' time you will 
have all the observations needed for a new value of the obliquity of 
the ecliptic. True, its accuracy may not be such that the government 
astronomers will ask to use it in place of the refined determinations of 
Le Verrier and Hansen, but your practical knowledge of an elementary 
principle by which the obliquity is found will be worth the having. 

Following are readings made in this manner at Am- 
herst, Massachusetts : — 



Arc-Reading 


Arc-Reading 


Obliquity 


June 20, 7i°.2 


Subtract December 22, 24^.3 = 46°.9 


23°45 


21, 71 .0 


21, 24 .0 = 47 .0 


23-5 


22, 70 .9 


20, 24 .1 = 46 .8 


234 



Mean value of obliquity = 23*^ 27' 

Explanation of the Equation of Time. — The reason may 
now be apprehended why mean sun and real sun seldom 



Explanation of Equation of Time 1 5 1 



AIEAN SUN IS HERE 



cross the meridian together. It is chiefly due to two inde- 
pendent causes, (i) The orbit in which our earth travel? 
round the sun is an elHpse. Motion in it is variable — 
swiftest about the ist of January, and slowest about the 
1st of July. On these dates, the equation of time due 
to this cause vanishes. Nearly intermediate it has a mean 
rate of motion; therefore at these times (about ist April 
and 1st October), 
the true sun -and 
the fictitious sun 
must both travel 
at the same rate in 
the heavens. But 
the real sun has 
been running ahead 
all the time since 
the beginning of 
the year, as this 
figure shows ; so 
that on the ist of April, the equation of time, from this 
cause alone, is eight minutes. The sun is slow by this 
amount because it has been traveling eastward so rapidly. 
On 1st October it is fast a like amount, because it has 
been moving very slowly through aphelion in the summer 
months ; therefore the real sun comes to the meridian 
earlier than it should, and it is said to be fast. 

(2) The second cause is the obliquity of the ecliptic. 
Suppose that the sun's apparent motion in the ecliptic 
were uniform : near the solstices its right ascension would 
increase most rapidly, because the hour circles converge 
toward the celestial poles just as meridians do on the earth. 
The case is like that of a ship sailing due east or west at 
a uniform speed : when in high latitudes she ' makes longi- 
tude ' much faster than she does near the equator. As 




AMONG 

Relation of True Sun to Mean Sun 



152 The Earth Revolves Rotcnd the Siui 

due to the second cause the equation of time vanishes four 
times a year ; twice at the equinoxes and twice at the sol- 
stices. At intermediate points (about the 8th of February, 
May, August, and November), the sun is alternately slow 
and fast about 10 minutes. Combining both causes gives 
the equation of time as already presented in the table on 
page 113. It is zero on 15th April, 14th June, ist Sep- 
tember, and 24th December. The sun is slowest (i4|- 
minutes) about nth February, and fastest (i6|- minutes) 
about 2d November. Attention is next in order turned to 
that remarkable yearly variation in conditions of heat 
and cold in our latitudes, called the seasons. 

The Seasons in General. — Those great changes in outward nature 
which we call the seasons are by no means equally pronounced every- 
where throughout our extended country. It is well, therefore, to 
sketch them in outline, from a naturalist's point of view, which is quite 
different from that of the astronomer. The earliest peoples noted 



Na ne f Eclipii c 




Pole ' ^ 

Earth's Axis inclined 662^ to the Plane of its Orbit 

these variations for practical purposes, chieily seedtime and harvest. 
But as men grew past the necessities of mere living, they began to ob- 
serve the natural beauty of each season as it came. Not knowing what 
occasioned the unvarying succession of these fixed, yet widely different 
conditions of the year, all sorts of fanciful explanations were invented. 
Clearly it is not the simple nearness or distance of the sun. as we ap- 
proach or recede in our orbit, which causes our changing seasons, 
for in our winter we are. as has already been said. 3.000.000 miles 
nearer than in summer. But as earth passes round the sun in its yearly 
path, the axis, remains always from year to year practically parallel to 
itself in space (neglecting the effect of precession), its inclination to the 
ecliptic being 66j- as shown in the outhne figure above. Alternately, 
then, the poles of earth are tilted toward and from that all-potent and 
heat-giving luminary. So in the sunward hemisphere summer pre- 
vaUs because of accumulated heat : more is received each dav than is 



The Seasons 153 

lost by radiation each night. But in the hemisphere turned away from 
the sun for the time, gradually temperature is lowered by withdrawal of 
life-giving warmth, more and more each day. Medium temperatures' 
of autumn follow, and eventually it becomes midwinter. 

Spring and Summer. — But when, by the earth's journeying onward 
in its orbital round, the pole again becomes tilted more and more to- 
ward the sun, soon an awakening begins. The melting of ice and 
snow, the gradual reviving of brown sods, the flowing of sap through 
branches apparently lifeless, the mist of foliage beginning to enshroud 
every twig until the whole country is enveloped in a soft haze of palest 
green and red, gray and yellow, — all these are Nature's signs of spring. 
Biologists tell us that this vegetal awakening comes when the tem- 
perature reaches 44^ Fahrenheit. Soon come the higher temperatures 
requisite for more mature development, and midsummer follows rapidly. 
The astronomer can, of course, say just when in June our longest day 
comes — when the sun rises farthest north and sets farthest north, 
thereby shining more nearly vertically upon us at noon, and remaining 
above the horizon as long as possible ; when daylight lasts with us 
until long past eight o'clock, and in England and Scotland until nearly 
ten. But wlio can divine just when the country stands at the fullest 
flood tide of summer, with the rich growth of vegetation, tangled 
masses of flowers and foliage, roadsides crowded with beauty, the 
shimmer of heat above ripening fields, perfecting grains, and early 
fruits? Or when it first begins to ebb? That is for another observer 
no less subtile than the astronomer with his measuring instruments and 
geometric demonstrations. Very different, too, is the time in different 
places ; often there is a wide range of local conditions which modify 
greatly the effects produced by purely astronomical causes. 

Autumn and Winter. — Thoreau, that keen observer of times and 
seasons, used always to detect signs of summer's waning in early July. 
But persons in general notice few of the advance signals of a dying 
year. Not until falling leaves begin to flutter about their feet, and 
grapes and apples ripen in orchard and vineyard, do they realize that 
autumn is really' here — that season of fulfillment, when everything is 
mellow and finished. Our hemisphere of the earth is turning yet 
farther away from that sun upon which all growth and development 
depend. When trees are a glory of red and yellow and russet brown, 
when corn stands in full shocks in fields, and day after day of warmth 
and sunshine follow through royal October, — it seems impossible to 
believe that slowly and surely, winter can be approaching. But soon 
chilly winds whistle through trees from which the bright leaves are 
almost gone ; a thin skim of ice crystals shoots across wayside pools 
at evening, and speedily shivering winter is upon us. Just before 
Christmas, this part of our earth is tipped its farthest away from the 



154 ^^^ Earth Revolves Round the Sun 

sun. Then, for a few days, the hours of darkness are at their longest. 
The sap has withdrawn far into the roots of trees until the cold shall 
abate ; leaden skies drop snowflakes, and earth sleeps under a mantle 
of white. Cold is apt to increase for a month after the sun has actually 
begun to journey northward. His rays, warm and brilliant, flood every 
nook and crevice in leafless forests ; but where is their mysterious 
power to call life into bare branches, to wake the flowers, and stir the 
grass ? It is almost startling to think that a permanent withdrawal of 
even a slight amount of the sun's warmth would freeze this fair earth 
into perpetual winter — that a small change in the tilt of our axis 
might make arctic regions where now the beauty of summer reigns in 
its turn. But the laws of the universe insure its stability ; and changes 
of movement or direction are very slow and gradual, so that all our 
familiar variation of seasons, each with its own charm, cannot fail to 
continue for more years than it is possible to apprehend. In late Janu- 
ary, weeks after our hemisphere has begun again to turn sunward, even 
the most careless observer notes the lengthening hours of daylight, and 
knows that spring is coming. That thrill of mysterious life w^hich this 
earth feels at greater warmth, and the quiet acceptance of its with- 
drawal, have been celebrated by poets in all ages ; and the astronomer's 
explanations of whys and wherefores cannot add to these marvelous 
changes anything of beauty or perennial interest, although they may 
conduce to completeness and precision of statement. 

Explanation of the Change of Seasons. — So much for 
mere description : the explanation has already been hinted. 
Our change of season is due to obhquity of the echptic, 
or to the fact that the axis of our planet, as it travels round 
the sun, keeps parallel to itself, and constantly inclined to 
its orbit-plane by an angle of 66^-"^. The opposite illustra- 
tion should help to make this clear. 

Beginning at the bottom of the figure, or at midsummer, it is appar- 
ent how the earth's northern pole is tilted toward the sun by the full 
amount of the obliquity, or 23^°. It is midsummer in the northern 
hemisphere, also it is winter in the southern, because the south pole is 
obviously turned away from the sun. Passing round to autumn, in 
the direction of the large arrows, reason for the equable temperatures 
of that season is at once apparent : it is the time of the autumnal equi- 
nox, or of equal day and night everywhere on the earth, and the sun's 
rays just reach both poles. Going still farther round in the same direc- 
tion, to the top of the illustration, the winter solstice is reached ; it is 



Most Heat at Midday 



155 



northern winter because the north pole is turned away from the sun 
and can receive neither light nor heat therefrom ; also the southern hem- 
isphere is then enjoying summer, because the south pole is turned 23^° 
toward the sun. Again moving quarter way round, to the left side of the 
illustration, the season of spring is accounted for, and the temperature 
is equable because it is now the vernal equinox. Another quarter 
year, or three months, finds the earth returned to the summer solstice ; 
and so the round of seasons runs in never-ending cycle. 



IT.IS.NOWTHE 
-• VERNAL 

"equinox 




IT IS. NOW THE 

AUTU_MiJAL_ry5 FIRST 
EQUINOX ' OF ARIES 



View of Earth's Orbit from the North Pole of the Ecliptic 

Earth receives most Heat at Midday. — It is necessary to 
examine into the detail of these changes of light and heat 
a little more fully. Every one is aware how much warmer 
it usually is at noon than at sunrise or sunset, mostly be- 
cause of change in inclination of the sun's rays from one 
time of day to another. Any surface becomes the warmer, 



156 The Earth Revolves Round the Sun 

the more nearly perpendicularly the sun's rays strike it, 
simply because more rays fall upon it. 



In the figure, ab^ cd, and ef are equal spaces, and R is the bundle 

of solar rays falling upon them. Obviously more rays fall upon cd than 

upon ab, because the rays are parallel. But the 

^^^ ^-- - ^ lessened warmth of sunrise and sunset is partly 

^^^H 6 ^ due to greater absorption of solar heat by our 

^^Kk ^ ^ atmosphere at times when the sun is rising and 

^^^H M^= setting, because its rays must then penetrate 

W^^H y a much greater thickness of the air than at 

^^^B^ ^ ^p E noon. Suppose the observer to be located 
within the tropics, because there the sun^s rays 
may be perpendicular to the earth's surface, as 
show^n in the diagram below^, while in our lati- 
tudes they never can be quite vertical even at 
midsummer noon. There the sun's rays may 
travel vertically downward at apparent noon ; and it is evident from 
the illustration that a beam of sunlight of a given width KL traverses 
only that relatively small part of the earth's atmosphere included be- 
tween KL^ MN, Now at sunrise observe the different conditions under 
which a beam of sunlight of the same breadth as KL is obliged to trav- 
erse the atmosphere. Observe, too, how much more atmosphere 
ABCD this beam must pass through. As the sun's energy is absorbed 



A Surface receives most 
Rays when they fall 
Perpendicularly upon 
it 




The Solar Beams are spread out and absorbed at Sunrise and Sunset 

in heating this greater volume of air, evidently the amount of heat arriv- 
ing at the earth's surface, CD^ where we are directly conscious of it, 
must be less by the amount which the atmosphere has absorbed. Be- 
sides this the amount of solar heat which falls upon a given area betw^een 
C and D will evidently be less than that received by an equal area be- 
tween M and N^ in proportion as CD is greater than MN. Like con- 
ditions prevail at sunset as shown. 



Most Heat at the Slimmer Solstice 157 




The United States as seen from the Sun 
in Midwinter 



Our Latitudes receive most Heat at the Summer Sol- 
stice. — In an earlier chapter it was explained how the. 
sun, by its motion north, crosses higher and higher on 
our meridian every day, from the winter solstice to the 
summer solstice. Just as 
each day the heat received 
increases from sunrise to 
noon, and then decreases to 
sunset, so the heat received 
at noon in a given place of 
middle north latitude, increases from the winter solstice to a 
maximum at the summer solstice. Also the sun's diurnal arc 
has all this time been increasing, so that a given hour of 
the morning, as nine o'clock, and a given hour of the after- 
noon, as three o'clock, places the sun higher and higher. 
The heat received, then, increases for two independent 
though connected reasons: (i) the sun culminates higher 
each day, and (2) it is above the horizon longer each day. 
The illustration (page 30) makes both reasons clear. The 

greater length of daytime 
exerts a powerful influence 
in modifying the summer 
temperatures of regions in 
very high latitudes w^here 
the summer sun shines con- 
tinually through the 24 
hours. For example, at the 
summer solstice, the sun 
pours down, during the 24 
hours, one fifth more heat upon the north pole than upon 
the equator, where it shines but 12 hours. So it is not 
easy to calculate the relative heat received at different 
latitudes, even if we neglect absorption by the atmos- 
phere. With this effect included, the problem becomes 




The United States as seen from the Sun 
in Midsummer 



158 The Earth. Revolves Round the Sun 



more complicated still. If earth and atmosphere could 
retain all the heat the sun pours down upon them, the 
summer solstice would mark also the time of greatest 
heat. But in our latitudes radiation of heat into space 
retards the time of greatest accumulated heat more than 
a month after the summer solstice. For evidently the 
atmosphere and the earth are storing heat so long as the 
daily quantity received exceeds the loss by radiation. For 
a similar reason, the time of greatest cold, or withdrawal 
of warmth, is not coincident with the winter solstice, but 
lags till the latter part of January. 

Accumulation ceases when Loss equals Gain. — Illustration by a 
three weeks' petty cash account should make this apparent. You start 

with 50 cents cash in hand. For 

the first week, you receive 25 
cents Monday, and spend 15 ; 30 
cents Tuesday, and spend 18; 
and so on, receiving five cents 
more each day, and spending 
three cents more than the day 
before. At the end of the week 
you will have $1.40. The sec- 
ond week, your receipts and ex- 
penditures are equal in amount 
to the first, but reversed as to 
days — your allowance is 50 
cents Monday, and you spend 
30 ; 45 cents Tuesday, and you 
spend 27 ; and so on. On the 
second Saturday your expense 
account will be the same as for 
the first Monday — you receive 
25 cents and spend 15 ; but your 
accumulated wealth will then be 
$2.30. The third week you 
receive 25 cents iMonday, 20 
cents Tuesday, and so on, but through the week you spend 1 5 cents 
each day. For two weeks your income has steadily been falling off, 
from 50 cents daily to nothing ; but your total cash in hand kept on 
accumulating, and did not begin to decrease until the middle of the 



§2.50 
.40 
.30 
.20 
.10 

§2.00 
.90 
.80 
.70 
.60 


FIRST WEEK 


SECOND WEEK 


THIRD WEEK j 






1 




































/ 








\ 






















/ 










\ 


















/ 












\ 
















/ 




























} 


/ 




























/ 




























/ 






























/ 




























Ui 


1 




















.40 










^/ 




















































.20 








y 1 


























c 


^/ 
























§1.00 
.90 
.80 
.70 
.60 
.50 






^ 






























/ 




























/ 






























/ 




























/ 
































































.0^ 




S 


■^ 


















.30 
.20 


'1> 




ft 


1 


^Tv, 














'^•'^.S^?^ 




^ 






^>- 


-^ 










^ 


















N; 






.10 







^< 


\ 


















i>^ 


^ 


1 1 


r \ 


H 1 


r 


- s 


M ^ 


'■ V 


V 1 


r 


- s 


M 1 


- V 




r 


= ^ 



Cash increases till Expenses and Income 

are Equal 



The Seasons Geographically 159 

third week, and on the third Saturday you close the account with $2.15 
in hand. Cash in hand at the beginning is the temperature about 
the middle of May, and the end of the first week corresponds to the 
summer solstice. Income is the amount of heat received from the 
sun, and expenditure is the amount radiated into space. Just as cash 
in hand went on accumulating long after receipts began to fall off, so 
the average daily temperature keeps on rising for more than a month 
after the solstice, when the amount received each day is greatest. The 
diagram shows the entire account at a glance, and illustrates at the same 
time a method of investigation much employed in astronomical and other 
researches, called the graphical method. Its advantages in presenting 
the range of fluctuations clearly to the eye are obvious. 

The Seasons Geographically. — The astronomical division 
of the seasons has already been given in the figure on 
page 155. It is as follows: — 

Spring, from the vernal equinox, three months. 
Summer, from the summer solstice, three months. 
Autumn, from the autumnal equinox, three months. 
Winter, from the winter solstice, three months. 

But according to the division among the months of the 
year, as commonly recognized in this part of the world, 
each season precedes the astronomical division by nearly 
a month, and is as follows : — 

Spring = March, April, May. 

Summer = June, July, August. 

Autumn — September, October, November. 

Winter = December, January, February. 

Differences of climate and in the forward or backward 
state of vegetable life, in part dependent upon local condi- 
tions, have led to different divisions of the calendar months 
among the seasons, varying quite independently of the 
latitude. Great Britain's spring begins in February, its 
summer in May, and so on. Toward the equator the 
difference of season is less pronounced, because the an- 
nual variation of the sun's meridian altitude is less ; and 
as changes in rainfall are more marked than those of 



i6o The Earth Revolves Round the Sun 

temperature, the seasons are known as dry and rainy, 
rather than hot and cold. These marked differences of 
season are recognized by the division of the earth's sur- 
face into five zones. 

Terrestrial Zones. — From the relation of equator to eclip- 
tic, and from the sun's annual motion, it is plain that thrice 
every year the sun must shine vertically over every place 
whose latitude is less than 23^°, whether north or south. 
This geometric relation gives rise to the parallels of lati- 
tude called the tropics ; the Tropic of Cancer being at 23 J° 
north of the equator, and the Tropic of Capricorn at 23^° 
south. They receive their names from the zodiacal signs in 
which the sun appears at these seasons. The belt of the 
earth included between these small circles of the terrestrial 
sphere is called the torrid zone. Its width is 47°, or nearly 
3300 miles. Similarly there are zones around the earth's 
poles where, for many days during every year, the sun 
will neither rise nor set. These polar zones or caps are 
also 47° in diameter. Between them and the torrid zone 
lie the two temperate zones, one in the northern and one 
in the southern hemisphere, each 43°, or about 3000 miles 
in width. The sun can never cross the zenith of any place 
within the temperate zones. If equator and ecliptic were 
coincident, that is, if the axis of the earth were perpen- 
dicular to the plane of its path round the sun, day and 
night would never vary in length, and our present division 
into zones would vanish. 

The Seasons of the Southern Hemisphere Our earth 

in traveling round the sun preserves its axis not only 
at a constant angle to the plane of its orbit, but always 
for a limited period of years pointing to nearly the same 
part of the heavens, as shown in the figure on page 65. 
Plainly, then, the seasons of the southern hemisphere must 
occur in just the order that our northern seasons do. In 



Seasons of the Southern Hemisphere i6i 

its turn the south pole incHnes just as far toward the sun 
as the north one does. But in so far as astronomical con- 
ditions are concerned, the southern seasons will be dis- 
placed just six months of the calendar year from ours. 
The following figures of the earth at solstices and equi- 
noxes make these relations clear. Midwinter in the south- 





Midsummer in the Southern Midsummer in the Northern 

Hemisphere Hemisphere 

ern hemisphere comes in June and Juh^, and Christmas 
falls in midsummer. The opening of their spring comes 
in August and September, and autumn approaches in 
February and ^larch. But while in the northern hemi- 
sphere the difference between the heat of midsummer and 
the cold of midwinter is somewhat lessened by the chang- 
ing distance of the sun, in the southern hemisphere this 
effect is intensified, because the earth comes to perihelion 
in the southern midsummer. However, on account of the 
sw^ifter motion of the earth from October to March than 







Spring in the Northern Spring in the Southern 

Hemisphere Hemisphere 

from April to September, the southern summer is enough 
shorter to compensate for the sun's being nearer, so that 
the southern summer is practically no hotter than the 
northern. On the other hand, the southern winter not 
only lasts about seven days longer than the northern, but 

TODD'S ASTRON. — II 



1 62 The Earth Revolves Romid the Sun 



it is colder also, because the sun is then farthest away. 
The range of. difference in the heat received at perihelion 
and aphelion is about -^^ part of the total amount. 

Annual Aberration. — In looking from a window into a 
quiet, rainy day, the drops are seen to fall straight down 



,^.1^% 





Aberration of the Raindrop is Greater as the Body moves Swifter 

earthward from the sky. But if, instead of watching from 
shelter, you go out in the rain and run swiftly through it, 
the effect is as if the drops were to slant in oblique lines 
against the face. For the man under the awning, the 
leisurely boy with rubber coat and hat on, and the courier 
caught in the rain, how different the direction from which 
the drops seem to come. A similar but even more exag- 
gerated effect may be* watched in a railway train speeding 
through a quiet snowstorm ; it seems as if the flakes sped 
past in an opposite direction, in white streaks almost hori- 



The Constant of Aberration 163 



J 



zontal, — the result of swift motion of the train, combined 
with that of the slowly falling snow. This appearance is 
called aberration, and in reality the same effect is produced 
by the progressive motion of light. Now replace the mov- 
ing train by the earth traveling in its orbit round the sun, 
and let the falling raindrop or snowflake represent the 
progressive motion of light ; then as the angle between 
the plumb-line and the direction from which rain or snow 
seems to come is the aberration of the descending drop or 
flake, so the angle between the true position of the sun 
and the point w^hich its light seems to radiate from is the 
annual aberration of light. It is usually called aberration 
simply, and was discovered by Bradley in 1727. 

The Constant of Aberration. — Notice two things : {a) that 
raindrop and snowflake both appear to come from points 
in advance of their true direction ; {U) that this angle of 
aberration is less as the velocity of the falling drop or flake 
is greater. The snowflake falls very slowly in comparison 
with the speed of the train, so the angle of aberration was 
observed to be perhaps 80° or more ; but where the velocity 
of the raindrop w^as nearly the same as the speed of the 
train, the angle of aberration w^as only 45°. Now imagine 
the velocity of the drop increased enormously, until it is 
10,000 times greater than the speed of the train : then we 
have almost exactly the relation which holds in the case of 
the moving earth and the velocity of a wave of light. In 
a second of time the earth travels i8|- miles, and light 
186,300 miles. But w^e found that any object which fills 
an angle of i^' is at a distance equal to 206,000 times its 
own breadth ; so that the angle of annual aberration of the 
sun must be the same as that filled by an object at a dis- 
tance of only 10,000 times its own breadth. This angle is 
2o'^5, and it is called the constant of aberration. It cor- 
responds to the mean motion of the earth in its orbit. At 



164 The Earth Revolves Round the Sun 



aphelion, where this motion is slowest, the sun's aberration 
drops to 20^'^ ; at perihelion, where fastest, it rises to 2o|''. 
The constant of aberration has been determined with great 
accuracy from observations of the stars ; and its exact cor- 
respondence with the motion of the earth may be regarded 
as indisputable proof of our motion round the sun. 

Aberration of the Stars. — Aberration is by no means 
confined to the sun ; but it affects the apparent position 
of the fixed stars as well. Observation shows that every 
star seems to describe every year in the sky a small ellipse. 
These aberration ellipses traversed by the stars all have 

equal major axes; that 
is, an arc of 41^', or 
double the constant of 
aberration. But their 
minor axes vary with 
the latitude, or distance 
of the star from the 
ecliptic. Try to con- 
ceive these ellipses in 
the sky; the major 
axis of each one coin- 
cides with the parallel 
of latitude through the 
star, and their size is 
such that they are just 
beyond the power of human vision. About 50 aberration 
ellipses placed end to end with their major axes in line would 
reach across the disk of the moon. For a star at the pole of 
the ecliptic, the minor axis is equal to the major axis ; that 
is, the star's aberration ellipse is a circle 41^^ in diameter. 
As shown in the illustration, the ellipses grow more and 
more flattened, for stars nearer and nearer the ecliptic ; 
and when the star's latitude is zero, the aberration ellipse 




Aberration Ellipses of the Stars 



The Calendar 165 

becomes seemingly a straight line, but actually a small arc 
of the ecliptic itself, 41^' in length. In calculating all- 
accurate observations of the stars, a correction must be 
applied for the difference between the center of the ellipse 
(the star's average place), and its position in the ellipse on 
the day of the year when the observation was made. Every 
star partakes of this motion, and thus proof of earth's mo- 
tion round the sun becomes many million fold. 

The Year. — Just as there are two different kinds of day, 
so also there are two different kinds of year. Both are 
dependent upon the motion of the earth round the sun, 
but the points of departure and return are not the same. 
Starting from a given star and returning to the same star 
again, the earth has consumed a period of time equal to 
365 d. 6 h. 9 m. 9 sec. This is the length of the sidereal year. 
But suppose the earth to start upon its easterly tour from 
the vernal equinox, or first of Aries: while the year is 
elapsing, this point travels westward by precession of the 
equinoxes, so that the earth meets it in 20 m. 23 sec. less 
than the time required for a complete sidereal revolution. 
This, then, is the tropical year, and its length is equal to 
365 d. 5 h. 48 m. 46 sec. It is the ordinary year, and 
forms the basis of the calendar. Another kind of year, 
strictly of no use for calendar purposes, is called the 
anomalistic year, and is the time consumed by the earth 
in traveling from perihelion round to perihelion again. 
We saw that the line of apsides moves slowly forward, 
at such a rate that it requires 108,000 years to complete 
an entire circuit of the ecliptic. The anomalistic year, 
therefore, is over 4I minutes longer than the sidereal 
year, its true length being 365 d. 6 h. 13 m. 48 s. 

The Calendar. — Two calendars are in use at the present 
day by the nations of the world : the Julian calendar and 
the Gregorian calendar. 



1 66 The Earth Revolves Round the Su 



n 



The former is named after Julius Caesar, who, in B.C. 46, reformed the 
calendar in accordance with calculations of the astronomer Sosigenes. 
The true length of the year was known by him to be very nearly 365^ 
days ; so Csesar decreed that three successive years of 365 days should 
be followed by a year of 366 days perpetually. But as the Julian year 
is 1 1. 2 minutes too long, the error amounts to about three days every 
400 years. In the latter part of the i6th century, the accumulation of 
error amounted to 10 days. Pope Gregory XIII corrected this, and 
established a farther reform, whereby three leap-year days are omitted 
in four centuries. Years completing the century, as 1900 and 2000, are 
ce7ttii7^ial years . Every year not centurial whose number is exactly divisi- 
ble by 4 is a leap year ; but centurial years are leap years only when 
exactly divisible by 400. The year 1900, then, is not a leap year, but 
the year 2000 is. In 1752 England adopted the Gregorian calendar, and 
earlier dates are usually marked o. s. (old style). At the same time, 
England transferred the beginning of the year from 25th March to ist 
January, the date adopted by Scotland in 1600, and by France in 1563. 
Thus before 1752, dates between ist January and 24th March fell in dif- 
ferent years in England and in Scotland or France, and frequently both 
years are written in early English dates — as 23d January, I7|f, the lower 
figure indicating the year according to Scotch and French, and the 
upper to early English, reckoning. Russia and Greece still employ the 
Julian calendar. Dates in these countries are usually written in frac- 
tional form ; for example, July ||, the numerator referring to the Julian 
calendar, and the denominator to the Gregorian. The year 1900 is, 
therefore, a leap year in Russia and Greece, and their difference of reckon- 
ing from ours is 13 days through the 20th century. 

The Week. — It embraces seven days, and has been 
recognized from the remotest antiquity. Its days are : — 

The Days of the Week 



English 


Symbol 


Derivation 


French 


German 


Sunday 





Sun's day 


Dimanche 


Sontag 


Monday 


3) 


Moon's day 


Lundi 


Montag 


Tuesday 


/ 


Tuisco's day 


Mardi 


Dienstag 


Wednesday 


? 


Woden's day 


Mercredi 


Mittwoch 


Thursday 


% 


Thor's day 


Jeudi 


Donnerstag 


Friday 


9 


Freya's day 


Vendredi 


Freitag 


Saturday 


\ 


Saturn's day 


Samedi 


Sonnabend 



Reformz7zg the Calendar 167 

Tuisco is Saxon for the deity corresponding to the Roman Mars, 
Woden for Mercury, Thor for Jupiter, and Freya for Venus ; therefore 
the symbols of the corresponding planets were adopted as designating 
the appropriate days of the week. These symbols are more often used 
in foreign countries than in our own. The relation of the week to the 
year is so close (52 x 7 = 364) as to suggest a possible improvement in 
the calendar. 

Memorizing the Days in the Month. — To many persons 
the varying number of days in the months of our year is 
a great inconvenience. This time-worn stanza is sometimes 

helpful : — 

Thirty days hath September, 

April, June, and November ; 

All the rest have thirty-one. 

Save February, which alone 

Hath twenty-eight, and one day more 

We add to it one year in four. 

The facts are there, even if the rhythm cannot be defended. An 
easier method of memorizing the succession is apparent from the illus- 
tration below : Close the hand and count out the months on the 
knuckles and the depressions between them, until July is reached, then 
begin over again. The knuckles represent long months, and the de- 
pressions short ones. 

Reforming the Calendar. — The inconveniences of our present Gre- 
gorian calendar are many. Some authorities think it on the whole no 
improvement on the Julian 
calendar ; and certainly much 
confusion would have been 
avoided, if the Julian cal- 
endar had been continued 
in use everywhere. A re- 
turn to the Julian reckoning 
at the beginning of the 20th 
century, ist January, 1901, 
has been suggested by New- 
comb, the eminent Amer- 
ican astronomer ; but such a 
change could be brought 
about only by wide international agreement. An obvious change hav- 
ing many advantages would be the division of the year into 13 months, 
each month having invariably 28 days, or exactly four weeks. Legal 
holidays and anniversaries would then recur on the same days of the 



JANUARY )^ 
AUGUST J ^ 




FEBRUARY "l 

SEPTEMBER/... X. 




MARCH 1 " •-.. ''^- ^^m. 

OCTOBER /"---.., - (■ , 
APRIL 1 (^ 

NOVEMBER ; ;, 

MAY 1 ..- ' ^ ^s^ 
DECEMBER J 


V 


JUNE 1 '' .. ' 


^^^ 


JULY -s/ 




To recall the Number of Days 


in Each Month 



1 68 The Earth Revolves Round the Sun 

week perpetually. The chief difficulty would arise in the proper dispo- 
sition of the extra day at the end of each ordinary year ; and of two 
extra days at the end of each leap year. 

Easter Sunday. — Easter Day is a movable festival, because it falls 
on different days in different years. By decree of the Council of 
Nicaea, a.d. 325, Easter is kept on the Sunday which falls next after 
the first full moon following the 21st of March. If a full moon falls 
on that day, then the next full moon is the Paschal moon ; and if the 
Paschal moon itself falls on Sunday, then the next following Sunday 
is Easter Day. Many have been the bitter controversies about the 
proper Sunday to be observed as Easter Day, in years when the rule 
was from the nature of the case ambiguous. Easter Day is not, how- 
ever, determined by the true sun and moon, but by the motion of the 
fictitious sun and of a fictitious moon imagined to travel uniformly with 
the time, and to go once round the celestial equator, in exactly the 
same time that the real bodies travel once round the heavens. Conse- 
quently the above rule must frequently fail, if applied to the phases of 
the moon as given in the almanac. Following are the dates of Easter 
for about a quarter century : — 

Easter Day, i 890-1913 



Year 


Date 


Year 


Date 


Year 


Date 


Year 


Date 


1890 


April 6 


1896 


April 5 


1902 


March 30 


1908 


April 19 


1891 


March 29 


1897 


April 18 


1903 


April 12 


1909 


April 1 1 


1892 


April 1 7 


1898 


April 10 


1904 


April 3 


I9I0 


March 27 


1893 


April 2 


1899 


April 2 


1905 


April 23 


I9II 


April 16 


1894 


March 25 


1900 


April 15 


1906 


April 15 


I9I2 


April 7 


1895 


April 14 


I90I 


April 7 1907 


March 31 


I9I3 


March 23 



Having now learned the A B C's of the language which 
astronomers use, and having studied the earth as a revolv- 
ing globe and the seeming motions of the stars relatively 
to it; also having ascertained many facts connected with 
our yearly journey round the sun, — we may next seek 
to apply that knowledge in a long voyage, begun early 
in December, from New York to Yokohama by way of 
Cape Horn. 



CHAPTER VIII 

THE ASTRONOMY OF NAVIGATION 

ON an actual voyage to Japan and back, we shall in- 
vestigate new astronomical questions in the order 
of their coming to our notice, and verify many 
astronomical relations founded on geometric truth. So 
we shall be learning a cosmopolitan astronomy of use in 
foreign countries as well as at home, and acquiring some 
knowledge of astronomical methods by which ships are 
safely guided across the oceans. 

Navigation. — Navigation is the art of conducting a ship 
safely from one port to another. When a ship has gone 
20 miles out to sea, all landmarks will usually have disap- 
peared, and the sea horizon will extend all the way round 
the sky. Look in whatsoever direction we will, nothing 
can be seen but an expanse of water (page 25), appar- 
ently boundless in extent. Outside the ship there is 
nothing w^hatever to tell us where we are, or in what 
direction to steer our craft. Every direction looks like 
every other direction. Still the accurate position of the 
ship must be found. The only resource, then, is to 
observe the heavenly bodies, and their relation to the 
horizon. 

The navigator must previously have provided himself ^Yith the lesser 
instruments necessary for such observation : and the technical books 
and mathematical tables by means of which his observations are to be 
calculated. These processes of navigation are astronomical in charac- 
ter, and the principles involved are employed on board every ship. 

169 



lyo 



The Astronomy of Navigation 



The computations required in ordinary navigation are based upon the 
data of an astronomical book called the N'aiitical Almanac. 

The Nautical Almanac. — The Nautical Almanac contains the accu- 
rate positions of the heavenly bodies. They are calculated three or 
four years in advance, and published by the leading nations of the 
globe. Foremost are the British, American, German, and French Nau- 
tical Almanacs. Below is a part of a page of The American Ephejneris 



and Nautical Abnanac for 



showino; data relatino: to the sun. 



October, 1899 







AT 


GREENWICH APPARENT NOON 






^ 


^ 






Sidereal 




^ 






% 

a; 

ft 




THE SUN'S 


Time of 
Semi- 
diam- 
eter 
Passing 
ISIerid- 
ian 


Equation 
of Time, 

to be 
Subtracted 

from 
Apparent 

Time 


3 



Q 


Apparent 

Right 
Ascension 


.SI 

M H 


Apparent 
Declination 


Diff. 

for 

I 

Hour 


Semi- 
diameter 


ft 






h. m. s. 


s. 


' '/ 


" 


. // 


s. 


m. s. 


S. 


SUN. 


I 


122939.39 


9.058 


S. 3 12 15.5 


-58.27 


161.37 


64-37 


10 19.23 


0.796 


Mon. 


2 


1233 16.94 


9.071 


3 35 33-0 


58.18 


16 1.64 


64.41 


1038.18 


0.783 


Tues. 


3 


123654.82 


9.085 


35848.0 


58.07 


16 I.9I 


64.46 


1056.81 


0.769 


Wed. 


4 


124033.03 


9.099 


422 0.3 


—57-95 


16 2.19 


64.51 


II 15.10 


0-755 


Thur. 


5 


1244 11.59 


9.II4 


4 45 9-4 


57.81 


162.47 


64.56 


II 3304 


0.740 


Frid. 


6 


124750.52 


9.130 


5 814.9 


57-65 


162.75 


64.62 


II 50.61 


0.724 


Sat. 


7 


12 51 29.84 


9.147 


531 16.5 


-57-48 


163.03 


64.68 


12 7.80 


0.708 


^-^'A^. 


8 


1255 9.56 


9.164 


55413-8 


57-29 


163.31 


64.74 


1224.59 


0.691 


Mon. 


9 


125849.70 


9.182 


617 6.4 


57-09 


16 3.60 


64.80 


1240.96 


0.673 



The intervals here are one day apart ; but for the moon, which moves 
among the stars much more rapidly, the position is given for every hour. 
Also the angular distance of the moon from certain stars and planets is 
given at intervals of three hours. Upon the precision of the Nautical 
Almanac depends the safety of all the ships on the oceans. Besides 
the figures required in navigating ships, the Nautical Almanacs contain 
a great variety of other data concerning the heavenly bodies, used by 
surveyors in the field and by astronomers in observatories. 

The Ship's Chronometers. — Some hours before the departure of the 
vessel, two boxes about a foot square are brought on board with the 
greatest care, and secured in the safest part of the ship, where the tem- 
perature will be nearly constant. Within each box is another, about 
eight inches square, shown open in the picture opposite. Inside it is a 
large watch, very accurately made and adjusted, forming one of the 
most important instruments used in conducting ships from port to port. 



Chronometers 



171 



It is called the marine chronometer, or box chronometer, but generally 
the chronometer simply. The face, about 4^ inches in diameter, is 
usually dialed to 12 hours, as in ordinary watches. In addition to the 
second hand at the bottom of the face, there is a separate index at the 
top to indicate how many hours the chronometer has been running 
since last wound up ; for, like all good watches, winding at the same 
hour every day is essential. 
Spring and gears are so re- 
lated that a chronometer 
ordinarily runs 56 hours, 
though it should be wound 
with great care at regular 
intervals of 24 hours — the 
extra 32 being a concession 
to possible lapses of mem- 
ory. Other chronometers, 
wound regularly every week, 
are constructed to run an 
extra day, and so are called 
^eight-day' chronometers. 
All these instruments are so 
jeweled that they will run 
perfectly only when the face 
is kept horizontal ; they are 
therefore hung in gimbals, a 
device with an intermediate 
ring, and two sets of bearings 
with axes perpendicular to 
each other. As the chro- 
nometer case is hung far above its center of gravity, its face always 
remains horizontal, no matter what may be the tilt of the outer box, 
in consequence of the rolling or pitching of the ship. The instrument 
shown in the illustration is of that particular type known as a break- 
ci7'Ciiit chronometer, so called because an electric circuit (through wires 
attached to the two binding posts on the left side of the box) is auto- 
matically broken at the beginning of every second, by means of a very 
delicate spring attached alongside one of the arbors. Such a chronom- 
eter is generally employed by surveying expeditions in the field, where 
a chronograph (page 213) is needed to record the star observations, 
and where a clock would be too bulky and inconvenient. 

What the Chronometers are for. — The real purpose of chronometers 
is to carry Greenwich time, and the need of this is made clear farther 
on. For at least a fortnight before they are brought on board ship, all 
chronometers are carefully tested and compared with a standard clock, 




The Chronometer 



172 The Astronomy of Navigation 

regulated by frequent observations of the sun and stars, usually at 
some astronomical observatory. So at the outset of our voyage we 
see how intimate is the relation between practical astronomy and the 
useful art of navigation. The navigator of the ship is provided with a 
memorandum for each chronometer, showing how much it is fast or 
slow on Greenwich time, and how much it is gaining or losing daily. 
The amount by which it is fast or slow is called the chronometer error 
or correction ; and the rate is the amount it gains or loses in 24 hours. 
If the chronometer is a good one and well adjusted, the rate should be 
only a small fraction of a second. As a rule, on voyages of moderate 
length, the Greenwich time can always be found from the chronometers 
within three or four seconds of the truth. This uncertainty amounts 
to about a mile in the position of the ship. To avoid the possibility, of 
entire loss of the Greenwich time by any accident to a single chronom- 
eter, ships nearly always carry two, and often many more. 

The Works of the Chronometer. — Familiarity with the interior of any 
watch will help in understanding the finer and more complicated works 




Works of the Chronometer (Size compared with Ordinary Watch) 

of the chronometer, well shown in the illustration. The ordinary watch 
alongside indicates the relative size of the parts. The chronometer 
balance is about one inch in diameter, and the hairspring about \ inch 
in diameter, and \ inch high. Fusee, winding post, and some other de- 
tails are well seen. On the left is the glass crystal, set in a brass cell 
which screws on top of the brass case, shown on the right. On the 
right-hand side of this case is seen one of the pivot bearings by which 
it swings in the gimbals. 

The Chronometer Balance. — A balance compensated for temperature 
is necessary to the satisfactory running of a chronometer, because a 
chronometer with a plain, uncompensated brass balance will lose 6\ 
seconds daily for each Fahrenheit degree of rise in temperature. In 



Time on Board Ship 



^IZ 



order to counteract this effect, marine chronometers (and all good 
watches) are provided with a balance, the principle of which is shown 
in the illustration. The arm passing centrally through the balance is 
of steel, and at its ends are two large-headed screws, for making the 
chronometer run correctly at a 
standard temperature, say 62°. 
The semicircular halves of the 
rim are cut free, being attached 
to the arm at one end only. 
The rim itself is composed of 
strips of brass and steel firmly 
brazed together. The outer 
part is brass, and the inner 
steel, of one half the thickness of 
the brass. With a rise of tem- 
perature, brass tends to expand 
more rapidly than steel ; and 
by overpowering the steel, it 
bends the free ends of the rim 
inward, practically making the 
balance a little smaller. When 
the temperature falls, the balance 

enlarges again slightly. Near the middle of each half rim is a weight, 
which can be moved along the rim. Delicate adjustment for heat and 
cold is effected by trial, the chronometer being subjected to varying 
temperatures in carefully regulated ovens and refrigerating boxes. The 
weights are moved along the rim until gain or loss is least, no matter 
what the thermometer may indicate. 

Time on Board Ship. — The time for everybody on board ship is 
regulated according to an arbitrary division adopted by navigators. 
The day of 24 hours is subdivided into six periods of four hours each, 
called watches. A watch is a convenient interval of duty for both 
officers and sailors ; and this division of the ship's day is recognized 
by mariners the world over. The period from 4 p.m. to 8 p.m. is sub- 
divided into two equal parts, called dogwatches ; so that the seven 
watches of the ship's day, with their names, are as follows : — 




The Chronometer Balance 



The first watch. 
The mid watch, 
The morning watch, 
The forenoon watch, 
The afternoon watch, 
The first dogwatch. 



from 8 P.M. to 12 midnight, 

from 12 midnight to 4 a.m. 
from 4 A.M. 
from 8 A.M. 
from 12 noon 
from 4 P.M. 



The second dogwatch, from 6 p.m. 



to 8 A.M. 

to 12 noon. 

to 4 P.M. 

to 6 P.M. 

to 8 P.M. 



174 The Astronomy of Navigation 

The dogwatches differ in length from the regular watches, so that 
during the cruise the hours of duty for officers and men may be dis- 
tributed impartially through day and night. Every watch pf four hours 
is again divided into eight periods, each a half hour long, called bells. 
Each watch, except the dogwatches, therefore, continues through eight 
bells. The end of the first half-hour period of each watch is called one 
bell', of the second, two bells ; of the third, t/wee bells; and so on. 
Four bells, for example, corresponds to two o'clock, six o'clock, and ten 
o'clock ; and seven bells to half past three, half past seven, and half 
past eleven, whether a.m. or p.m., of time on shore. 

Low Tide delays the Ship's Departure. — Another point of 
contact between astronomy and navigation was well illus- 
trated as the ship was about to depart. The tide was low, 
and she must wait a few hours until it rose. The times of 
high tide and low tide are predicted by calculations based 
in large part upon the labors of astronomers. The mere 
phenomena of tides are inquired into here, leaving the 
explanation of them to a subsequent chapter on universal 
gravitation. 

The Tides in General. — A visit of one day to the seashore 
is sufficient to show the rising and falling of the ocean. It 
may happen that in the morning a walk can be taken 
along the broad, sandy beach, which later in the day will be 
covered under the risen waves. Or rocks where one sat in 
the morning are in the afternoon buried underneath green 
water. A single day will always show these changes ; and 
another single day will exhibit similar fluctuations, only at 
other hours. The photographic picture opposite indicates 
a typical range of the tides, and horizontal markings on 
the rocks show the level of high tide, seven or eight feet 
above water level in the illustration. A week's stay at the 
shore will establish the regularity of variation. High tide 
at ten o'clock in the morning means low tide a little after 
four in the afternoon, or approximately six hours later, 
high tide occurs again soon after ten in the evening, and 
low tide at about half past four in the morning. So there 



The Tides Defined 



175 



are two high tides and two low ones in every 24 hours, or 
more properly, in nearly 25 hours. And if it is high tide 
one morning at ten o'clock, the next day full tide will occur 
at about eleven o'clock. So that gradually the times of 
high and low tide change through the whole 24 hours, lag- 
ging about 50 minutes from one day to another. 





At Low Tide — (Markings on Rocks are Level of High Tide) 

The Tides defined. — A tide is any bodily movement of 
the waters of the earth occasioned by the attraction of 
moon and sun. The word tide^ as used by the sailor, 
often refers to the nearly horizontal flow of the sea, forth 
and back, in channels and harbors. To the astronomer, 
the word tide means a vertical rise and fall of the waters, 
very different in different parts of the earth, due to the 
westerly progress of the tidal wave round the globe. The 
time of highest water is called high tide ; and of lowest 
water, low tide. From high tide to low is termed ebb tide ; 
from low to high, flood tide. Near new moon and full 
moon each month (as explained on page 388) occur the 
highest and lowest tides, termed spring tides. As the 
moon comes to new and full every month, or lunation, and 
as there are about I2| lunations in the year, there are 
nearly 25 periods of spring tides annually. Spring tides 



176 



The Astronomy of Navigation 






have nothing to do with the season of spring. Intermedi- 
ate and near the moon's first and third quarters, the ebb 
and flood, being below the average, are called' neap tides 
{nipped, or restricted tides). So valuable to the navigator 
is a knowledge of the times of high tide and low tide 
at all important ports, that these times are carefully calcu- 
lated and published by government authority a year or 
two in advance. This duty in our country is fulfilled by 
the United States Coast and Geodetic Survey, a bureau of 
the Treasury Department. 

Direct and Opposite Tides. — The tide formed on the 
earth as a whole is made up of two parts : {a) the direct 
tide, which is the bulge or protuberance, or tidal 
wave on the side of the earth toward the tide- 
raising body, and {U) the opposite tide, which is 
the tidal wave on the side away from it. The 
figure shows a section of the earth surrounded 
as it always is by such a double tide. Gravita- 
tion, as explained in the chapter on that subject, 
elongates the watery envelope of the earth very 
slightly in two opposite directions. Thus the 
earth and its waters are a prolate spheroid ; that 
is, slightly football-shaped. As the earth turns 
round on its axis eastward, this watery bulge 
seems to travel from east to west, in the form 
of a tidal wave twice every 25 hours. To illus- 
trate : It is as if a large cannon ball were turn- 
ing on the shorter axis of a football and inside 
Opposite Tides ^f j^^ jf ^^ watcrs couM at once respond to 
the moon's attraction, the time of high tide would coincide 
with the moon's crossing the upper or lower meridian. 
But on account of inertia of the water, the comparatively 
feeble tide-producing force requires a long time to start 
the wave. The time between moon's meridian transit and 








Direct and 



Movement of the Tidal Wave 177 

arrival of the crest of the tidal wave is called the establisli- 
ment of the port. This is practically a constant quantity 
for any particular port, but is different for different ports. 
It is 8 J hours for the port of New York. 

Only the Wave Form travels. — Guard against thinking that the 
tides are produced by the waters of the ocean traveling bodily round 
the globe from one region to another. The deep waters merely rise 
and fall, their advance movement being very slight, except where the 
tidal wave impinges upon coasts. It is only the form of the wave that 
advances westerly. Illustrate by extending a piece of rope on the floor 
and shaking one end of it. A wave runs along the rope from one end 
to the other ; but only the w ave form advances, the particles of the 
rope simply rising and falling in their turn. So with the waters of 
the tidal wave. 

Movement of the Tidal Wave. — Originating in the deep 
waters of the Pacific Ocean, off the west coast of South 
America, the tidal wave travels westerly at speeds varying 
w4th the depth of the ocean. The deeper the ocean, the 
faster it travels. During this progressive motion of a 
given tidal wave it combines with other and similar tidal 
waves, so that the resultant is always complex. In about 
12 hours it reaches New Zealand, passes the Cape of 
Good Hope in 30 hours, where it unites w^ith {a) the 
direct tide in the Atlantic off Africa, and (b) a reversed 
wave, which has moved easterly round Cape Horn into 
the Atlantic. The united wave then travels northwesterly 
through the Atlantic Ocean about 700 miles hourly, reach- 
ing the east coast of the United States in 40 hours. On 
account of the irregular contour of ocean beds, there is 
never a steadily advancing tidal wave, as there would 
be if the oceans covered the entire earth to a uniform 
depth. Tidal charts of the oceans have drawn upon them 
irregularly curved lines connecting places where crests of 
tidal waves arrive at the same hour of Greenwich time. 
These are called cotidal lines. 

TODD'S ASTROX. — 12 



1 78 The Astronomy of Navigation 

Extent of Rise and Fall. — The extent of rise and fall of the tide 
varies in different places. Speaking generally, in mid-ocean the differ- 
ence between high and low water is between two and three feet, while 
on the shores of great continents, especially in shallow and gradually 
narrowing bays, the height is often very great. The average spring 
tide at New York is about 5^ feet, and at Boston about 11. In the 
Bay of Fundy, spring tides rise often 60 feet, and sometimes more. 
The tide also rises in rivers, but less as the distance from the river's 
mouth increases, where it is more and more neutralized by the current. 
A tide of a few inches advances up the Hudson River from New York 
to Albany in about nine hours. It is possible for a river tide to rise to 
a higher level than that of the ocean itself, where the momentum of the 
wave is expended in raising a relatively small amount of water, on 
the principle of the hydraulic ram. At Batsha in Tonquin there is no 
tide whatever, because the waters enter by two mouths or channels 
of unequal depth and length, the lagging in the longer channel being 
about six hours m.ore than in the shorter one. 

Tides in the Great Lakes. — Theoretically there are tides in large 
bodies of inland water also ; but even the largest lakes are too small 
for their share in the moon's tide-producing force to be very pronounced. 
A tide of less than two inches occurs in Lake Michigan at Chicago ; 
and in the Mediterranean there is a slight tide of about 18 inches. 
Height of the tide in landlocked seas depends in part upon the ratio 
of the length of such seas (east and west) to the diameter of the earth. 
Meager tides like these are often completely masked by the tides which 
local winds raise. 

Duration of Flood and Ebb Tides. — In mid-ocean the 
tidal wave rises much less than on the coasts ; for on 




Direction of advance of tidal 
Ebb Tide always longer than Flood Tide 

reaching shallow water, friction retards the wave, shorten- 
ing its length from crest to crest, and greatly increasing 
the height of the tide, particularly if the advancing wave 
is forced to ascend a somewhat shallow and gradually 
narrowing channel. 

Above figure illustrates this change in the section of a tidal wave 
advancino^ toward a coast on the rio^ht. The crest of the wave is farther 



Diurnal Inequality of the Tides 179 

from the bottom and therefore less retarded by friction, so that it 
advances more rapidly, and makes the wave steeper on its front than 
on its after slope. Under all ordinary conditions, then, flood tide is 
evidently shorter in duration than ebb tide. At Philadelphia, for 
example, where the difference is accentuated by coast configurations 
ebb tide is nearly two hours longer than flood tide. An extreme case 
is that known as the tidal bore, in which the advancing slope of the 
tidal wave in certain favorably conditioned rivers becomes perpendicular. 




^^^^^:^ 




,.»\^.^.4.^^^^ 





Tidal Bore at Caudebec, a town on the Seine (according to Flammarion) 

The crest then topples over, and flood tide takes the form of a swiftly 
advancing breaker ; in only a few minutes the waters rise from low to 
high, and ebb tide consumes rather more than 12 hours following. This 
strong tidal wave surmounting the seaward current of the river, some- 
times piling up a cascade of overlapping waves, is well marked in the 
Seine, the Severn, and the Ganges. 



Diurnal Inequality of the Tides. — If the earth's equator 
coincided with the plane of the moon's orbit, and if there 
were no obliquity of the ecliptic, evidently the tide-produc- 



I So 



The Astronomy of Navigation 



ing force of both sun and moon -would always act perpen- 
dicular to the earth's axis. The direct tide and the opposite 
tide would then be symmetrical with reference to the 
equator ; and, generally speaking, equal latitudes would 
experience equal tides. When, however, the moon is at her 



S Y M 



S Y M 



S V M 




Diurnal Inequality of the Tides at San Francisco 

greatest declination north, the direct tide is highest at those 
north latitudes where the moon culminates at the zenith ; 

w^hile the opposite tide is slight in the northern hemi- 
sphere, but highest at the antipodes of the direct tide, or 
in south latitudes equal to the north declination of the 
moon. This difference in height of the two daily tidal 
weaves is called the diurnal inequality. 

In the case of lunar tidal waves, the diurnal inequality becomes 
zero twice each month, when the moon crosses the celestial equator; 
and the diurnal inequality of the solar tide vanishes at the equinoxes. 
But this obvious dirterence in height of the two daily tides is greatly 
moditied by coast configurations and other conditions. The illustration 
above is plotted from a fortnight's record of the tide gauge at San 
Francisco. The wave line represents the rise and fall of the surface 
of the water: the distance from one horizontal line to another being 
two feet. Vertical lines divide off periods of 24 hours, the succession 
of days being indicated at the top. The difference between direct and 
opposite tide is very marked each day. except when the moon is near 
the equator, w-hen the diurnal inequahty is much reduced. Small dots 
are placed adjacent to the highs and lows of the direct tide, which 
illustrate the diurnal inequality excellently, having a very wide range 
in northern latitudes when the moon culminates nearest the zenith, a 
medium range when she is crossing the equator, and a minimum range 
when her south declination is near a maximum. 



The Sextant 



i8i 




The Sextant. — The sextant is a light, portable instru- 
ment arranged for measuring conveniently arcs of a great 
circle of the celestial sphere in any plane whatever. With 
it are made the astronomi- 
cal observations which are 
calculated by means of the 
Nautical Almanac. Next 
to the compass, the sex- 
tant is more frequently 
used than any other in- 
strument; for by the 
angles measured with it, 
the navigator finds his 
position upon the ocean 

from day to day. Sextant for measuring Angle? 

In navigation the sextant is generally used in a vertical plane ; that 
is, in measuring altitudes of heavenly bodies. The sextant was in- 
vented by Hadley in 1730. A finely graduated arc A, of 60° (whence 
the origin of its name) has an arm (from /downward toward the right) 
sliding along it, as the radius of a circle would, if pivoted at the center - 
and moved round the circumference. Rigidly attached to the pivot 
end of this moving arm, and at right angles to the plane of the arc, is 
a mirror, /, called the index glass. Also firmly attached to the frame 
of the arc is another mirror, FH^ only partly silvered, called the 
horizon glass. A telescope K^ parallel to the frame and pointed 
toward the center of horizon glass, helps accuracy of observation. 
Shade glasses of different colors and density (at D and E) make it 
possible to observe the sun under all varying conditions of atmosphere 
— haze, fog, thin cloud, or a perfectly transparent sky ; for that orb 
is, of all heavenly bodies, the most frequently observed in navigation. 
Shade glasses tone down the light, whatever its intensity, and farther in- 
crease the accuracy of observation. A clamp and tangent screw (below 
the arc) facilitate the details of actual observation ; antecedent to 
which, however, the adjustments of the sextant must be carefully made. 
The most important are these : when the arm is set at the zero of the arc, 
the plane of the principal mirror also must pass through the zero of the 
arc ; and the horizon glass must be parallel to the mirror, both being 
perpendicular to the plane of the graduated arc or limb. The horizon 
line is C// (page i82\ and the heavenly body is in the direction CS. 



l82 



The Astronomy of Navigation 



The distant horizon is seen by the eye through the telescope at K^ and 
its Hne of sight passes through the upper or unsilvered part of the hori- 
zon glass LL . When the arm is 
at o°, the index glass stands in the 
direction AK\ but when an altitude, 
HCSj is to be measured, the arm 
is pushed along the limb to O. 
The index glass then stands in the 
position I/' J so that light will travel 
in the direction of the arrows SABK. 
After reflection from the two mir- 
rors, the object will appear in contact 
with the horizon. The arc is read, 
and the observation is complete. 
As the angle between index and 
horizon glasses is half the angle 
measured, the limb is graduated at 
the rate of i° for each actual 30'. 




How Angles are measured 



Finding the Latitude at Sea. — Usually the first astro- 
nomical observation at sea will be made for the purpose of 
finding the latitude of the ship. There are many methods, 
but all are based on the fundamental principle already 
given, that the latitude is always equal to the altitude of 
the celestial pole. Usually latitude is found by observing 
the altitude of some celestial body when crossing the me- 
ridian on the opposite side of the zenith from the pole. 
So it is referred directly to the equator, whose distance 
from the zenith always equals the latitude also. 

For example : a few minutes before noon, the navigator will begin 
to observe the sun's altitude with the sextant, repeating the observation 
as long as the altitude continues to increase. When the sun no longer 
rises an}- higher, it is on the local meridian. The time is high noon, or 
apparent noon. The officer then gives the order ^ Make it Eight Bells,'' 
and proceeds to ascertain the latitude from the observation just made. 
The diagram on page 84 elucidates the principle involved. Once the 
meridian zenith distance is found by observation, latitude is ascertained 
from it by the same principle, whether at sea or on land. 

Finding the Longitude at Sea. — As on land, so at sea, 
finding the longitude of a place is the same thing as find- 



Dip of the Horizon 183 

ing how much the local time differs from the time of a 
standard meridian. The prime meridian of Greenwich is 
almost universally employed in navigation. First, then, 
local time must be found. 

A portable instrument like the sextant must be used, because of the 
continual motion of the ship. With it the navigator observes the alti- 
tude of some familiar heavenly body toward the east or west. This 
operation is called ' taking a sight.' Most often the sun is observed for 
this purpose — either early in the morning, or late in the afternoon. 
The nearer the time of its crossing the prime vertical, the better, because 
its altitude is then changing most rapidly, and so the observation can be 
made more accurately. First, the latitude must be known. Then the 
local time is worked out by a branch of mathematics called spherical 
trigonometry. This computation forms part of the everyday duty of the 
navigator ; and as simplified for his use, it is an arithmetical process, 
greatly facilitated by specially prepared tables of the relation of the 
quantities involved. These are three : the altitude of the body (given 
by observation), its declination (obtained from the Nautical Almanac), 
and the latitude of the ship. Having found the local time, take the 
diiference between it and the chronometer (Greenwich) time ; the result 
is the longitude sought. If local time is greater than Greenwich time, 
longitude is east; west, if less. There are many methods of ascertain- 
ing longitude, and each navigator, as a rule, has his favorite. Sumner's 
method is generally conceded to be the best. Except in overcast 
wxather, the navigating officer will usually feel sure of the position of his 
ship within two miles of latitude, and three to five miles of longitude. It 
is difficult to find her position nearer than this unless the observations 
are themselves made with exceptional care, and the errors of sextant 
and chronometer have been specially investigated wdth greater precision 
than is either usual or necessary. Once the position of the ship is 
known, it is plotted on the chart, and the proper course is calculated 
and the ship maintained on it by constant watch of the compass, a deli- 
cate magnetic instrument by which true north can always be found. 

Dip of the Horizon. — In calculating any observation of 
altitude of a heavenly body taken at sea, a correction for 
dip of the horizon is always applied. Dip of the hori- 
zon is the angle between a truly horizontal line passing 
through the observer's eye, and the line of sight to his 
visible horizon, or circle which bounds the view. 



1 84 



The Astronomy of Navigation 



As the surface of our globe may be regarded as spherical (always 
so considered in practical navigation), it must curve down from the 
ship equally in every direction. The figure shows this clearly. Also, 
as altitude is angular distance above the sensible horizon, it is apparent 
that every observation of altitude must be diminished by the correction 
for dip. Plainly, too, dip is greater, the higher the deck of the ship 
from which the observation is taken. If the deck is 12 feet above the 
water, the correction for dip is about three minutes of arc; if 18 feet, 
about four minutes. From the elevation of a deck of ordinary height, 
the visible horizon is about seven miles distant in every direction ; 




Dip of the Horizon 

and generally speaking a ship will never be visible at more than double 
this distance, even with a telescope. Usually an approaching ship will 
not become visible until about eight miles away ; but the condition 
of the atmosphere, the character of the distant ship's rigging, the way 
in which sunlight falls upon it, and the rising and falling of both ships 
on the waves, — all affect this distance materially. 

Where does the Southern Cross become Visible ? — A question of 
perennial interest to the southward voyager. Its answer may come 
appropriately now, but first it is necessary to know how far this famous 
asterism is south of the celestial equator ; that is, its south declination. 
Consulting charts of the southern heavens, we find that the central 
region of the Cross is in south declination 60°. Consequently, it will 
just come to the southern horizon when the latitude is equal to 90° 
— 60° ; that is, 30°. But haze and fog near the sea horizon will usually 
obscure the Cross until a latitude six or seven degrees farther south 
has been reached. Good views of it may be expected at the Tropic 
of Cancer, and they improve with the journey farther south. It must, 
however, be said that the Southern Cross is a disappointment, for it 
is by no means so striking- a configuration as the Great Bear. 

Where will the Sun be overhead at Noon ? — Not before 
we reach the tropics, because the sun never can pass over- 
head at any place whose latitude exceeds 23-|-°. 



Southern Circumpolar Stars 



185 



But in Chapter iv it was shown that the latitude is always equal to 
the declination of the zenith. If, therefore, it is desired to find the 
place where the sun will pass through the zenith at noon, we must 
first ascertain the sun^s declination from the almanac (or approximately 
from page 85). Then it is apparent that the zenith sun will be met at 
noon, when the latitude of the ship is exactly the same as the sun's 
declination. From vernal equinox to autumnal equinox, when the sun 
is all the time north of the equator, the ship must be in the northern 
hemisphere, in order that the sun may pass directly over her. And, 
in general, the sun will pass through the ship's zenith on the day when 
her latitude is the same in sign and amount as the declination of the 
sun. For example, on the 2d of March the sun will be overhead at 
noon to all ships which are crossing the 7th parallel of south latitude, 
because the sun's declination is 7° south on that day. 

In Southern Latitudes. — Looking northward, or away from the pole 
now visible, the stars appear to rise on our right hand, passing up over 
the meridian, and setting on 
our left. They still rise in the 
east and set in the west. But 
looking poleward, the stars cir- 
culate round the pole clockwise 
by diurnal motion, as indicated 
by arrows in the diagram adja- 
cent. The south pole of the 
heavens rises one degree above 
the south horizon for every 
higher degree of south lati- 
tude. If the south pole were 
actually reached, all the stars 
south of the equator would be 
perpetually visible, and no star 
of the northern hemisphere 
could ever be seen. But the 
region overhead in the sky 
would not be conspicuously 
marked, as at the north pole, 
by Polaris and the Little Bear, 
because there is no conspicuous 
south polar star. In fact, there is no star as bright as the fifth magni- 
tude within the circle drawn five degrees from the pole. The pair of 
stars in the Chamideon, here shown underneath the pole, are of the 
fifth magnitude, and Beta Hydri is a third magnitude star. All are 
easy to find from the Southern Cross, which is '2\ times farther from 
the pole than the Chamaeleon stars. 




SOUTH 



15 HORIZON 

IZ 



Apparent Motion of the South Polar Heavens 



1 86 The Astronomy of Navigation 

Rounding Cape Horn to San Francisco. — On the remainder of our 
ship's voyage to latitude about 57° south, where she rounded the Cape, 
little or nothing new arose, involving any astronomical principle. The 
Southern Cross passed practically through the zenith, because the lati- 
tude was nearly equal to the declination of the asterism. The mild 
temperature nearly all the way was a verification of the opposite 
season in the southern hemisphere ; for although it was winter (De- 
cember, January, and February) at home, it was summer at the same 
time in south middle latitudes. Approaching the equator, it was 
observed that the inequality of day and night was gradually obliterated, 
quite independently of the season ; for at the equator the diurnal arcs 
of all heavenly bodies are exact semicircles, no matter what their 
declination. At the equator, too, the brief twilight attracted attention — 
brief because the sun sinks at right angles to the horizon, instead of 
obliquely ; so that it reaches as quickly as possible the angle of depres- 
sion (18°) below the horizon, at which twilight ceases. On approaching 
the California coast, after a voyage of nearly four months, in which land 
had been sighted only once, it was a matter of much concern what the 
deviation of the chronometers might be from the rates established at 
New York. It was evidently not large, for the landfall off the Golden 
Gate was made without any uncertainty. On coming to anchor in San 
Francisco bay, it was easy to verify the chronometers, by observing the 
time signal at local noon (nearly) each day, which is given by the 
dropping of a large and conspicuous time ball at exactly 8 h. cm. os. 
P.M., Greenwich time. Comparison of the chronometers with this 
signal showed that the Greenwich time, as indicated by their dials, 
differed only 8s. from the time ball; so that the average daily devia- 
tion from the rate as determined at New York was only J^ of a second. 

Standard Time Signals. — About a dozen time balls are 
now in operation in the United States. The principal 
ones are dropped every day at noon, Eastern Standard or 
75th meridian time, in Boston, New York, Philadelphia, 
Baltimore, and Washington ; at noon, Central time, in 
New Orleans; and at noon. Pacific Standard, or 120th 
meridian time, in San Francisco. 

The error of the signal, only a fraction of a second, is published in 
the local newspapers of the following day. In foreign countries, time 
signals are now regularly furnished, chiefly for the convenience of ship- 
ping, in about 125 of the principal ports of the world. In England 
and the British possessions, it is customary to give the time signal at 



Where Does the Day Cliaiige? 187 

I P.M., often by firing a gun. But the dropping of a time ball (page 9) 
is the favorite signal throughout the world generally. In many of these 
ports, the time is determined with precision at a local observatory, and 
the time ball may be utilized in re-rating the ship's chronometers. 

Where does the Day change ? — Imagine a railway gir- 
dling the world nearly on the parallel of New York, and 
equipped with locomotives capable of maintaining a speed 
of 800 miles an hour. At noon on Wednesday, start west- 
ward from New York ; in about an hour, reach Chicago, in 
another hour Denver, in still another hour San Francisco. 
As these places are about 15°, or one hour of longitude 
from each other, evidently it will be Wednesday noon on 
arrival at each of them, and at all intermediate points, 
because the traveler is going westward just as fast as the 
earth is turning eastward ; so it will be perpetual midday. 
Continue the journey westward at the same rate all the 
way round the earth. Night will not come because the sun 
has not set. So there can be no midnight. How, then, 
can the day change from Wednesday to Thursday } Will 
it still be Wednesday noon when the traveler returns to 
New York .^ On arrival there, 24 hours after he started, 
he will be told that it is Thursday noon. Where did the 
day change } Manifestly it must change somewhere once 
every 24 hours. Nearly the whole world has agreed to 
change at the i8oth meridian from Greenwich, because 
there is little land adjacent to this meridian, and very few 
people are inconvenienced. Noon at Greenwich is mid- 
night on the 180th meridian. If, therefore, a ship westward 
bound on the Pacific Ocean comes to this meridian at mid- 
night of, say, Wednesday, on crossing that meridian it is 
immediately after 12 a.m. of Friday. As a rule ships will 
not arrive at the i8oth meridian exactly at midnight; but 
this does not affect the principle involved : a whole day, 
or 24 hours, is dropped or suppressed in every case. 



1 88 The Astro7io7ny of Navigation 

If, for example, it is Friday afternoon at four o'clock when this- line 
is reached, it becomes Saturday immediately after 4 p.m. as soon as 
the 1 80th meridian is crossed. This experience, familiar to all trans- 
pacific voyagers, is called ' dropping the day.' If a person born on 
the 29th of February were crossing the Pacific Ocean westward on a 
leap year, and should arrive at the i8oth meridian at midnight on the 
28th of February, the change of day would bring the reckoning of time 
forward to the first of March ; so that he would have the novel experi- 
ence of living eight years with strictly but a single birthday anniversary. 
Journeying eastward across the i8oth meridian, the reverse of this pro- 
cess is followed, and 24 hours are subtracted from the reckoning. If^ 
for example, the ship reaches this meridian at 10 a.m. Wednesday, it 
immediately becomes 10 a.m. Tuesday on crossing it. When, in 1867, 
the United States purchased Alaska, it was found necessary to set the 
official dates of the new territory forward 11 days (page 166), because 
the reckoning had been brought eastw^ard from Russia, its former owner. 

Time at Home compared with Time in Japan. — The 

arrival of a ship at Yokohama will usually be cabled to her 
owners, — in New York, very probably. Sending such 
a message naturally gives rise to inquiry as to when it 
will be received; for there is no cable across the Pacific 
Ocean, and the dispatch must cross Asia, Europe, and 
the Atlantic. The table of ' Standard Time in Foreign 
Countries' (page 126) shows that the time service of the 
Japanese Empire corresponds to the 135th meridian (9 
hours) east of Greenwich. As Eastern Standard time is 
five hours slower than Greenwich time, evidently Japan is 
10 hours west of our standard meridian ; and its standard 
time would be 10 hours slower than ours, except for the 
change of day. On account of this, the standard time of 
Japan is 24 hours in advance, minus 10 hours slower ; that 
is, 14 hours in advance of Eastern Standard time. 

The same result is reached, if we go round the world eastward to 
Japan, thereby avoiding the troublesome i8oth meridian. The Eastern 
Standard meridian is five hours west of Greenwich, and Japan is nine 
hours east of Greenwich. So that it is 14 hours east of us ; that is, its 
time is 14 hours faster than ours. Allow six hours of actual time for the 
transmission of a cablegram from Yokohama to New York ; if one 



Great Circle Courses 189 

were sent at 7 a.m. on Tuesday, it would be delivered at 11 p.m. on 
Monday, or seemingly eight hours before it was dispatched. 

Great Circle Courses the Shortest in Distance. — In ocean 
voyages, in steamships, particularly in crossing the Pacific, 
the captain will usually choose the course which makes 
his run the shortest distance between the two ports. Im- 
agine a plane through the center of the earth and both 
ports; the arc in which this plane cuts the earth's surface 
is part of a great circle. This arc, the shortest distance 
between the two ports, is called a great circle course. If 
both are on the equator, the equator itself is the great 
circle connecting them ; and the ship goes due east or due 
west, when sailing a great circle course from one to the 
other. If, however, the ports are not on the equator, 
but both in middle latitudes, as San Francisco and Yoko- 
hama, the parallel of latitude 
(which nearly joins them and 



is a small circle of the e-lobe) 

^ San Francisco Yokohama 



San I 

has a greater degree of cur- 
vature than the great circle, ^ ^^-'— ~~~~---^ ^ 

which clearly must pass San Frlnclsco Yokohama 

through much higher lati- Great circle course the Shortest 

tudes. As shown by the dia- 
gram of the two arcs, seen from above the pole, the great 
circle arc, lying farther north, deviates less from a straight 
line than the corresponding arc of a parallel (upper curve). 
It is therefore a shorter distance. Consequently ships 
sailing great circle courses will usually pass through lati- 
tudes higher than either the point of departure or des- 
tination. 

Before passing on to a study of sun, moon, and 
planets, we digress to consider the instruments by whose 
aid our knowledge of these orbs has mainly been ac- 
quired. 



CHAPTER IX 

THE OBSERVATORY AND ITS INSTRUiMENTS 

OBSERVATORIES are buildings in which astro- 
nomical and physical instruments are housed, and 
which contain all the accessories for their con- 
venient use. Most important of all instruments of a 
modern observatory are telescopes and spectroscopes. 

Astronomy before the Days of Telescopes. — The prog- 
ress of astronomy has always been closely associated with 
the development and application of mechanical processes, 
and skill. Earlier than the seventeenth century, the size of 
the planets could not be measured, none of their satellites 
except our moon were known, the phases of Mercury and 
Venus were merely conjectured, and accurate positions of 
sun, moon, and planets among the stars, and of the stars 
among themselves, were impossible — all because there 
were no telescopes. More than a half century elapsed 
after the invention of the telescope before Picard com- 
bined it with a graduated circle in such a way that the 
measurement of angles was greatly improved. Then arose 
the necessity for accurate time ; but although Galileo had 
learned the principles governing the pendulum, astronomy 
had to wait for the mechanical genius of Huygens before 
a satisfactory clock was invented, about 1657. Nearly all 
the large reflecting telescopes ever built were constructed 
by astronomers who possessed also great facility in practi- 
cal mechanics ; and the rapid and significant advances in 
nearly all departments of astronomy during the last half 

190 



Best Sites for Observatories 191 

century would not have been possible, except through the 
skill and patience of glass makers, opticians, and instru- 
ment builders, whose work has reached almost the limit of 
perfection. Before i860, if we except the meager evidence 
from meteoric masses of stone and iron, some of which had 
actually been seen to fall, it is proper to say that our igno- 
rance of the physical constitution of other worlds than ours 
was simply complete. The principles of spectrum analysis 
as formulated by Kirchhoff led the way to a knowledge of 
the elements composing every heavenly body, no matter 
what its distance, provided only it is giving out light in- 
tense enough to reach our eyes. But since Newton, no 
necessary step had been taken along this road until the 
way to this signal discovery was paved by the deftness of 
Wollaston, who showed that light could not be analyzed 
unless it is first passed through a very narrow slit ; and 
of Fraunhofer, the eminent German optician, who first 
mapped dark lines in the spectrum of the sun. So, too, 
in our own day the power of telescope and spectroscope 
has been vastly extended by the optical skill and mechani- 
cal dexterity of the Clarks and Rowland, Hastings and 
Brashear, all Americans. 

Best Sites for Observatories An observatory site 

should have a fairly unobstructed horizon, as much free- 
dom from cloud as possible, good foundations for the 
instruments, and a very steady atmosphere. 

All of these conditions except the last are self-evident. To realize 
the necessity of a steady atmosphere, look at some distant out-door 
object through a window under which is a register, a stove, or a radi- 
ator. It appears blurred and wavering. Similarly, currents of warm 
air are continually rising from the earth to upper regions of the at- 
mosphere, and colder air is coming down and rushing in underneath. 
Although these atmospheric movements are invisible to the eye, their 
effect is plainly visible in the telescope as blurring, distortion, quiver- 
ing, and unsteadiness of celestial objects seen through these shift- 



192 The Observatory and its Instruments 

ing air strata of different temperatures, and consequently of different 
densities. The trails on photographic star plates, exposed with the 
camera at rest, make this very evident. That a perfect' telescope may 
perform perfectly, it must be located in a perfect atmosphere. Other- 
wise its full power cannot be employed. All hindrances of atmosphere 
are most advantageously avoided in arid or desert regions of the globe, 
at elevations of 3000 to 10,000 feet above sea level. On the American 
continent have been established several observatories at mountain ele- 
vation, the most important being the Boyden Observatory of Harvard 




'i he Dearborn Observatory at tvanston, Professor G. W. Hough, Director 



College, Arequipa, Peru (8000 feet) ; the Lowell Observatory, Arizona 
(7000 feet) ; and the Lick Observatory, California (4000 feet). Higher 
mountains have as yet been only partially investigated ; and it is not 
known whether difficulties of occupying them permanently would more 
than counterbalance the gain which greater elevation w^ould afford. 

A Working Observatory. — Chief among exterior features is the great 
dome, usually hemispherical, and capable of revolving all the way 
round on wheels or cannon balls. The opening through which the 
telescope is pointed at the stars is a slit, two or three times as broad as 
the diameter of the object glass. The slit opens in a variety of ways, 
often as in the above picture, by sliding to one side on pivots and 
rollers. Solidly built up in the center of the tow^er is a massive pier, 
to support the telescope, wholly disconnected from the rest of the build- 
ing. By means of the universal or equatorial mounting (page 54), the 



Instruments Classified 193 

open slit, and the revolving dome, the telescope is readily directed 
toward any object in the sky. Observatories are provided with a 
meridian room, with a clear opening from north to south, in which a' 
transit instrument or meridian circle is mounted. Part of it shows at 
the right of the tower. Here also are the chronograph, and clock or 
chronometer for recording transits of the heavenly bodies. Modern 
observatories are provided with a library and computing room, a photo- 
graphic dark room, and other accessories of equipment, varying with 
the nature of their work. The best type of observatory construction 
utilizes a minimum of material, so that very little heat from the sun is 
stored in its walls during the day, and local disturbance of the air in 
the evening, caused by radiation of this heat, is but slight. Louvers 
and ivy-grown walls contribute much to this desirable end. It is con- 
sidered best to house each instrument in a suitable structure of its own, 
as remote as possible from many or massive buildings. 

Instruments classified. — Instruments used in astronomi- 
cal observatories are divided into three classes : — 

(a) Telescopes, or instruments for aiding or increasing 
the power of the human eye. There are two kinds, the 
dioptric, or refracting telescope, and the catoptric, or re- 
flecting telescope. 

{]?) Instrtimejtts for measuring angles. These, also, are 
subdivided into two kinds ; the arc-measuring instruments, 
like graduated circles, for measuring very large arcs, the 
micrometer for measuring very small ones, and the helio- 
meter for measuring arcs intermediate in value, as well 
as very small ones. The second class of instruments 
concerned in the measurement of angles are transit instru- 
ments for observing time (measured by the uniform angu- 
lar motion of a point on the equator), chronographs for 
recording the time, clocks and chronometers for carrying 
the time along accurately and continuously from day to 
day. 

{c) Physical instruments, of which many varieties are em- 
ployed in most modern observatories, for investigating the 
light and heat radiated from celestial objects. Chief among 
them are spectroscopes, or light-analyzing instruments, of 
todd's astron. — 13 



194 ^/^^ Observatory and its Instrumejtts 



which there are numerous forms, adapted to especial 
uses. Hehostats are plane mirrors moved by clockwork, 
for the purpose of throwing a reflected beam of light from 
a heavenly body in a constant direction. The bolometer 
is an exceedingly sensitive measurer of heat, and the 
thermopile is used for the same purpose, though much 
less sensitive. The photometer is used for measuring the 
light of the heavenly bodies. The actinometer and pyrhe- 
liometer are physical instruments used in measuring the 
heat of the sun. The photographic camera is extensively 
employed at the present day, to secure, by means of tele- 
scope, photometer, spectroscope, and bolometer, permanent 
record, unaffected by small personal errors to which all 
human observations are subject. 

Telescopes. — The telescope is an optical instrument for 
increasing the power of the eye by making distant objects 
seem larger and therefore nearer. 




Uiustrating the Visual Angle 

It does this by apparently increasing the visual angle. A distant 
object fills a relatively small angle to the naked eye, but a suitable 
combination of lenses, by changing the direction of rays coming from 
the object, makes it seem to fill a much larger angle, and there- 
fore to be nearer. Such a combination is called a telescope. The 
parts of all telescopes are of two kinds, — optical and mechanical. 
The optical parts are lenses, or mirrors, according to the kind of tele- 
scope ; and the mechanical parts are tubes, and various appliances for 
adjusting the lenses or mirrors, including also the machinery for point- 
ing the tube. All the different lenses used in telescopes are illustrated 
opposite (in section). One principle is the same in all telescopes: 
a lens or mirror (called the objective) is used to form near at hand 
an image of a distant object ; and between image and eye is placed 



Kinds of Telescopes 



195 



PLANO-CONVEX 



EQUI-CONVEX 



a microscope (called the eyepiece or ocular) for looking at the image — 
just as if it were a fly's wing, or the texture of a feather. The point to 
which the lens converges the parallel rays from a star is called the 
principal focus (illustra- 
tion below) . The central 
ray, which passes through 
the centers of curvature 
of the two faces of the 
lens, traverses a line called 
the optical axis. The 
plane passing through the 
principal focus perpendic- 
ular to the optical axis is 
called the focal plane. 
Objective and eyepiece 
must be so adjusted and 
secured that their axes 
shall lie accurately in a 
single straight line. If 
objective and eyepiece 
could be held in this posi- 
tion by hand, also at the 
right distance apart, there 
would be no need of a tube 




PLANO-CONCAVE 



EQUI-CONCAVE 



CONCAVO-CONVEX 



Lenses of Different Shapes (in Section) 

The tube is sometimes made square, as 
well as round, and is to be regarded simply as a mechanical necessity 




PRINCIPAL 
FOCUS 



A Convex Lens refracts Parallel Rays to the Principal Focus 

for keeping the optical parts of the telescope in proper relative position. 
Also the tube is of some use in screening extraneous light from the 
eyepiece, although that service is slight. 

Kinds of Telescopes. — As to the principal kinds of telescopes : 
{a) If the objective is a lens (in its simplest form an equi-convex 



196 The Observatory and its Instruments 



lens), then the image is produced by bending inward or refracting to 
the focus all rays of light which strike the lens ; and the telescope 
is called a refractor, or refracting telescope. This sort of instrument 
appears to have been first known in Holland, early in the seventeenth 
century ; also it was invented by Galileo in 1609, and first used by him 
in observing the heavenly bodies. If a telescope is to perform prop- 
erly, its object glass cannot be made of plate glass, because the eye- 
piece would reveal defects in it similar to those which the eye plainly 
sees in ordinary window glass. But the objective must be made of 
that finest quality known as optical glass. Through a perfect speci- 




Angle of Reflection equals Angle 
of Incidence 




Concave Mirror reflects Parallel 
Rays to Focus 



men of optical glass polished with parallel sides, a perpendicular ray 
of light will pass without appreciable refraction, and with very little 
absorption. (^) If the objective is a concave mirror or speculum, the 
image is then formed by reflection, to the focus, of all rays of light 
which fall upon the highly polished surface of the mirror, and the tele- 
scope is called a reflector, or reflecting telescope. The above figures 
show the principle involved, the angle of reflection being in every case 
equal to angle of incidence. An actual speculum may be regarded as 
made up of an infinite number of plane mirrors, arranged in a 
concave surface differing slightly from that of a sphere, and being 
in section a parabola (page 398). As shown in the next illustration 
t4^ focal point is halfway from mirror to center of curvature. 

Growth of the Refracting Telescope. — An ordinary convex lens, in 
converging rays of light to a focus, must refract them, or bend them 
toward the axis of the lens. But light is commonly composed of a 
variety of colored rays, ranging through the spectrum from red to 
violet. Soon after the invention of the telescope Sir Isaac Newton 
discovered by experiment that prisms do not bend rays of different 
color alike ; violet light is much more strongly refracted than red, and 
intermediate colors in different proportions, according to the kind of 
light employed. We may regard a lens as an infinitely large collec- 



Gro-ii.<th of Refracting Telescope 



197 



tion of tiny prisms. Clearly, then, a perfect telescope seemed to be 
an impossibility from the very nature of the case, because no single 
lens had power to gather all rays at a given focus, and could only 
scatter them along the axis — the focus for violet rays being nearest 
the object glass, and for the red farthest from it. However, by grind- 



> :^mm> 



OF CURVATURE 




Mrn^ > 

Focus halfway from Mirror to Center of Curvature 

ing the convex lens almost flat, so that its focal length became very 
great, this serious hindrance to development of the telescope was in 
part overcome, and many telescopes of bulky proportions were built 
during the 17th century, which were most awkward and almost im- 
possible to manipulate. Sometimes the object glass was mounted in 
a universal joint on top of a high pole, and swung into the proper 
direction by means of a cord, drawn taut by the observer who held 
the eye-lens in his hand as best he could. Telescopes wxre built over 



BEAM OF WHITE LIGHTS 



BEAM OF WHITE LIGHT 




A Prism both refracts and disperses White Light 

200 feet in length, and some obser\'ations of value were made wdth 
them, though at an inconceivable expenditure of time and patience. 
Newton concluded that it was hopeless to expect a serviceable tele- 
scope of this kind; so the minds of inventors were turned in other 
directions. 



198 The Observatory and its Instrume7tts 

Why a Single Lens is not Achromatic. — For the sake of clear ex- 
planation, regard the lens made up as in the last figure, so that a section 
of it is the same as a section of two triangular prisms placed base to base. 
Let two parallel beams of white light fall upon the prisms as shown. 
Each wdll then be refracted toward the axis of the lens, and at the same 
time decomposed into the various colors of the spectrum. Red rays 
being refracted least, their focus will be found farthest from the lens. 
Violet rays undergoing the greatest angular bending, their focus will 
be nearest the lens. Foci for the other colors will be scattered along 
the axis as indicated. If we consider the actual lens, with an infinitude 
of faces or prisms, the effect is the same. So that, speaking generally, 
it cannot be said that the lens brings the rays of white light to any 
single focus whatever, and the image of a white object will be variously 
colored, wherever the eyepiece may be placed. 

Principle of the Achromatic Telescope. — The two lenses 
of the objective must be of different kinds of glass : (i) a 
double-convex lens of crown glass, not very dense, which 
ordinarily the light passes through first ; (2) a plano-con- 
cave lens of dense flint glass, usually placed close to the 
crown lens in small telescopes. 



.^ — ^ / 1 


1 


i 


^^-\ FOCUS FOR 


A -'' 


1 




^,.„--^^CROWN LENS 



COMBINATION 



Illustrating Principle of Achromatic Object Glass 



Similar prisms of these two kinds of glass bend the rays about equally ; 
so that while the double-convex lens converges the rays toward the 
axis, the single or plano-concave diverges them again, by an amount 
half as great. So much for refraction merely ; and it is plain from the 
above figure that the double object glass must have a greater focal length 
on account of the diverging effect of the flint lens. Next consider 
the effect of the two lenses as to dispersion of light, and the colors 
which each w^ould produce singly. If we try equal prisms of the two 
kinds of glass, it is found that the flint, on account of its greater den- 
sity, produces a spectrum about twice as long a^ the crowm ; therefore 



Efficiency of Object Glasses 



199 




its dispersive power, prism for prism, is twice as great. Now a lens 
may be regarded as composed of a multitude of prisms, — a mosaic of 
indefinitely small prisms. Evidently, then, the plano-concave lens of 
flint glass, although it has only half the refracting power of the crown 
lens, will produce the same degree of color as the double-convex lens 
of crown glass. Therefore, the dispersion or color effect of the con- 
vergent crown lens is neutralized by the passing of the rays through 
the divergent flint lens, and a practically colorless image is the result. 
Thus is solved the important problem of refraction without dispersion, 
opening the way for the great refractors of the present day. 

History of the Achromatic Telescope. — Half a century after Newton, 
Hall in 1733 found that the color of images in the refractor could be 
nearly eliminated by making the object glass of two lenses 
instead of one, as just explained ; a significant invention 
usually attributed to Dollond, who about 1760 secured a 
patent for the same idea which had occurred to him in- 
dependently. Progress of the art of building telescopes 
was thus assured ; and the only limitation to size appeared 
to be the casting of large glass disks. About 1840, these 
obstacles were first overcome by glass makers in Paris ; 
but in the larger telescopes, a new trouble arose, inherent 
in the glass itself; for the ordinary form of double object 
glass cannot be made perfectly achromatic. An intense 
purple light surrounds bright objects, an effect of the sec- 
ondary spectrum, as it is called, because dispersion or 
decomposition of the crown glass cannot be exactly neu- 
tralized by recomposition of the flint. Farther progress, 
then, was impossible until other kinds of glass were in- 
vented. Recent researches by Abbe under the auspices 
of the German Government have led to the discovery of 
many new varieties of glass, by combining which object 
glasses of medium size have already been made almost 
absolutely achromatic. Hastings in America and Taylor 
in England have met with marked success. Some of the 
new objectives are made of two lenses, and others of three ; 
but there is great difficulty in procuring very large disks 
of this new glass. 

Efficiency of Object Glasses. — This depends upon two 
separate conditions : {a) the light-gathering power of 
an objective is proportional to its area. Theoretically a 
6-inch glass will gather four times as many rays as a 3-inch 
objective, because areas of objectives vary as the squares of their 
diameters. But practically the light of the larger glass will be some- 
what reduced, because of the thicker lenses ; for all glass, no matter 






I 



ii 



Achromatic 
Telescope 
(in Section) 



200 The Observatory and its Instruments 



how pure, is slightly deficient in transparency. In the same way, the 
light-gathering power of any lens may be compared with that of the 
naked eye. In the dark, the pupil of the average eye expands to 
a diameter of about \ inch. The ratio of its diameter to that of a 

3-inch glass is 15, as in 
the illustration (reduced 
i) ; so a star in a 3-inch 
telescope appears nearly 
225 times brighter than 
it does to the naked eye. 
Calculating in the same 
way the efficiency of the 
great 40-inch lens of the 
Yerkes Observatory, it is 
found to be 40,000 times 
that of the eye. Test 
light-gathering power by 
ascertaining the faintest 
stars visible in the tele- 
scope, and comparing with 
lists of suitable objects. 
(U) The defining power 
of an objective is partly 
its ability to show fine 
details of the moon and 
planets perfectly sharp 
and clear ; but more precisely it is the power of separating the component 
members of close double stars (page 452). This power varies directly 
with the size or diameter of object glasses, if they are perfect; that is 
a 6-inch glass will divide a double star whose components are o".8 
apart, whereas it will require a 12-inch glass to separate a double star 
of only o".4 distance. But defining power is quite as dependent upon 
perfection of the original disks of glass, as upon the skill and patience 
of the optician who has ground and polished them. A large defect of 
either makes a worthless telescope. 

Method of Testing a Telescope. — Unscrew the cell of the objective 
from the tube, but do not take the lenses out of the cell. If on looking 
through it at the sky, the glass appears clear and colorless, or nearly so, 
the light-gathering power may be regarded as satisfactory. Small 
specks and air bubbles will never be numerous enough to be harmful ; 
each only obstructs a small pencil of light equal to its arer.. The defin- 
ing power may be tested in a variety of ways. Following is the method 
by an artificial star : Point the telescope on the bulb of an ordinary 
thermometer which lies in the sunshine, 50 feet or more distant. Or 




Eye and Objective collect Rays in Proportion 

to their Areas 



A Small but Useful Telescope 



20I 



the convex bottom of a broken bottle of dark glass may be used, R in 
•the illustration. On focusing, an artificial star will appear, due to re- 
flection of the sun from the bulb, sometimes surrounded by diffraction • 
rings (^, below). Slide eyepiece inward and outward from focus, 



10. 



E ^ 





One Method of Testing a Telescope 

until bright point of light spreads out into a round luminous disk, 
B. This is called the spectral image. A dark center, when the eye- 
piece is pulled out, and a brighter central area when pushed in, show 
that curvature of the glasses is more or less imperfect. A spectral 
image having a piece cut out, or a brush of scattering light, is a sign 
of bad defects inherent in the glass itself. An excellent objective gives 
spectral images perfectly circular, and evenly illuminated 
throughout, B. Repeat these tests on stars of the first 
magnitude. Heat from a lighted lamp placed where shown 
will simulate many deleterious effects of a very unsteady 
atmosphere. A and B then become C and Z^, rays and 
spots of the latter being continually in motion. 

A Small but Useful Telescope. — By expending a few 
cents for lenses, a person of average mechanical ability 
may, by a few hours' work, become possessed of a telescope 
powerful enough to show many mountains on the moon, 
spots on the sun, satellites of Jupiter, and a few of the 
wider double stars. Buy from an optician two spectacle 
lenses, round rather than oval, and of very different pow- 
ers ; for instance. No. 5 and No. 30. These numbers 
express the focal lengths of the lenses. Fit together 
two pasteboard tubes so that one will slide inside the other quite 
smoothly. Their combined length must be about six inches greater 




Spectral 
Images 



202 The Observatory and its Instruments 

than the sum of the numbers of the two lenses. Blacken the inside 
of tubes, and attach the lenses to their outside ends. No. 30 being 
the objective, and pointed toward the object, the magnifying power of 
the two lenses, when separated by a distance equal to the sum of their 
focal lengths, will be equal to their ratio, or six diameters. It was with 
a telescope made in this way that the writer, when a boy of fourteen, 
got his first glimpse of the satellites of Jupiter. A few dollars will buy 
a good achromatic object glass (of perhaps two inches diameter) and a 
pair of suitable eyepieces (powers about 25 and 100). A suitable 
mounting for such telescopes has already been described on page 53. 
The most important optical requisite is stated at the middle of page 
195. On adjusting the lenses in the tube, a serviceable and convenient 
telescope will be provided, quite capable of showing the phases of 
Venus, the ring of Saturn, and numerous double stars. 

The Great Refractors. — At the head of the list stands 
the 40-inch telescope, 65 feet long, of the Yerkes Observa- 
tory (pages 7 and 15). More favorably located is its rival 
in size, the famous Lick telescope of 36 inches aperture, 
situated on the summit of Mount Hamilton, California, 
4300 feet above the sea. 

The mountings or machinery for both these great instruments were 
built in Cleveland, by Messrs. Warner & Swasey ; but the object 
glasses were made by the celebrated firm of Alvan Clark & Sons, of 
Cambridgeport, from glass disks manufactured in Paris. No optical 
glass of the highest quality has yet been made in America, the process 
being, in some essentials, secret. Steinheil of Munich is now construct- 
ing an objective of 31 J inches aperture, of the new glass, for the astro- 
physical observatory near Berlin. A glass of like dimension by Henry 
is at the Meudon Observatory, Paris. The Clarks have made also an 
objective of 30 inches aperture, mounted by Repsold, at the Russian 
Observatory of Pulkowa, near Saint Petersburg. A glass of equal size, 
figured by the Brothers Henry of Paris, is mounted at the splendid 
observatory founded by Bischoffsheim at Nice, in the south of France. 
A 29 inch by Martin is at the Paris Observatory. The next three tele- 
scopes were made at Dublin, by Sir Howard Grubb, one of 28 inches 
and one of 26 inches aperture, located at the Royal Observatory, Green- 
wich, and the other, of 27 inches, at Vienna. Following these in order 
are a pair of telescopes of 26 inches aperture, made by Alvan Clark & 
Sons, one of which is the principal instrument of the United States 
Naval Observatory, at Washington, and the other is located at the 
University of Virginia. Between the dimensions of 25 inches and 15 



Growth of the Reflecting Telescope 203 

inches there are about two dozen refracting telescopes in all, many 
of which were made by Alvan Clark & Sons, although Brashear of 
Alleghany, an optician of the first rank, has made an 1 8-inch glass, 
now^ at the University of Pennsylvania. Quite the opposite of re- 
flectors, it is noteworthy that most of the great refractors have been 
built in America: and that they have contributed in a more marked 
degree to the progress of astronomical science. 

Invention and Growth of the Reflecting Telescope. — If converging 
the rays of light by refraction could never make a perfect telescope, 
clearly the only method left was to gather them at a focus by reflection 
from a highly polished surface. Although this way of making a tele- 
scope seems to have been understood as early as 1639, still a quarter 
century elapsed before Gregory built the first one (1663). He used 



RAYS FROM 
A STAR 



GREGORIAN (Secondary Mirror Concave) 



RAYS FROM 
A STAR 



CASSEGRAINIAN (Secondary Mirror Convex) 



RAYS FROM 
A STAR 



..Jl 



NEWTONIAN (Eyepiece on side of tube) 
Three Types of Reflecting Telescope 

two concave mirrors as in the illustration ; the one large to form the 
image, and the other small to reflect the rays out of the tube to the 
eyepiece. Ten years later Cassegrain made a farther improvement, 
replacing the small concave mirror of Gregory by a convex one (shown 
in the illustration also). Both these forms of reflector have the advan- 
tage that the observer looks directly toward the object at which the 
telescope is pointed ; but there is a great disadvantage in that the center 
or best part of the mirror has to be cut away, in order to let the rays 
through it to the eyepiece. The mirror is left whole, and less of its 
light is sacrificed in the form invented by Newton (1672), who inter- 
posed a small flat miiTor, at an angle of 45^ with the axis of the larger 
mirror. This arrangement, most commonly used in reflecting tele- 
scopes at the present day, has a slight disadvantage in that the observer 
must look into the eyepiece at right angles to the direction of the ob- 
ject under examination (see figure) ; but a small right-angled or totally 



204 The Observatory and its Instruments 

reflecting prism is now universally employed in lieu of the little 
diagonal mirror, thereby saving a large percentage of light. A fourth 
form of reflector, first suggested by Le Maire, was used by Herschel, 
in the latter part of the i8th century; he tilted the speculum slightly, 
to bring its focus at side of tube. Axis of eyepiece is directed, not as 
in diagram below, but toward center of mirror. Tilting the mirror 
saves all light, but distortion of image is not easy to avoid. Recently 



,^-i 



%^ 



RAYS FROM 

A STAR 

^ ^ 



-y 



Le Mairean or Herschelian Reflecting Telescope 

the ^ brachy-telescope,' or short telescope, has been invented to over- 
come this difficulty, by second reflection from a small and oppositely 
inclined convex mirror. Down to the middle of the 19th century, 

specula were always made of an 
alloy, generally composed of 59 
parts of tin and 126 of copper. 
Specula are now almost univer- 
sally made of glass, with a very 
thin film of silver deposited 
chemically upon the front sur- 
face, not upon the back as in 
the common mirror. These 
telescopes are often called silver- 
on-glass reflectors. As the light 
does not pass through the glass, 
it may be much inferior in quality 
to that required for a lens. Be- 
cause less difficult to build, the 
great telescope of the future will 
probably be a reflector, although 
of inferior definition. Great re- 
fractors are. however, less clumsy 
The Great Paris Reflector (Martin) and more efl-ective for actual use. 




Reflectors and Refractors Compared 205 



The Great Reflecting Telescopes. — The largest, sometimes called the 
' leviathan,' was built by the late Lord Rosse in 1845 ^^ Birr Castle, 
Parsonstown, Ireland. The speculum is of metal, six feet in diameter, 
and about eight inches thick. Its excessive weight of four tons makes a 
very heavy mounting necessary. Lord Rosse's telescope is Newtonian 
in form. The giant tube is 56 feet long, and 7 feet in diameter. The 
next in size is a five-foot silver-on-glass reflector, built by Common 
in 1889 at Ealing, England. It is Cassegrainian in form, and the 
glass of the mirror is nearly one foot in thickness, in order to pre- 
vent flexure, or bending by its own weight. The Yerkes Observatory 
is constructing a reflector of equal size. In 1867 Thomas Grubb built a 
four-foot silver-on-glass * Gregorian " for the observatory at Melbourne, 
Australia, and it is perhaps the most convenient in use of all the 
great reflectors. In the latter part of the i8th century Sir William 
Herschel built numerous reflecting telescopes, among them one of four 
feet diameter, and another of half that size ; he made many important 
discoveries with them, but none are now in condition to use. Lassell, 
an eminent English astronomer, built two great reflectors, one of four 
feet, and the other of two feet aperture, which he used on the island 
of Malta, 1852-1865. Several reflectors, three 
feet aperture, have been constructed, the most 
important of which is owned by the present 
Lord Rosse ; also one by the Lick Observa- 
tory. At the Paris Observatory is a great 
silver-on-glass reflector of nearly four feet 
aperture ; and an instrument ten feet in diam- 
eter has been projected for the Paris Exposi- 
tion of 1900. It is interesting to note that 
none of these great instruments have been 
constructed in America. The largest reflector 
ever built in the United States is 28 inches 
in diameter. It was made by Henry Draper, 
New York, in 1871, and is now used at the 
Harvard Observatory. Among present 
builders of reflecting telescopes in America 
are Edgecomb of Mystic, Connecticut ; and 
Brashear, one of whose lesser instruments is 
pictured in the adjoining illustration. 

Reflectors and Refractors compared. — In 
reflectors of medium size, tarnish and de- 
terioration of the polished surface are the 
chief disadvantage. But the film of a mirror 
less than a foot in diameter is readily renewed. 
When freshly silvered, a 12-inch speculum will collect the same amount 




A Modern ' Newtonian ' 
Brashear 



2o6 The Observatory and its Instruments 

of light as a 12-inch object glass, loss by reflection from the former 
being about equal to loss by absorption in passing through the latter. 
Well figured and newly polished mirrors of no greater dimension than 
this usually perform excellently ; and there is a marked advantage from 
the gathering of rays of all colors at the same focus. But from 12 
inches upward, flexure of the mirror begins to cause difliculties which 
increase rapidly with the size of the speculum. The mirror may be 
given a perfect parabolic figure for the position in which it is polished ; 
but as soon as turned to another angle of elevation, gravity distorts 
its figure. As a result, rays from a star are not collected at a single 
point, but scattered round it. The larger the mirror, the greater this 
difficulty, becoming almost impossible to alleviate entirely. Glass 
mirrors, in order to be least afl'ected by it, should have a thickness 
equal to one sixth of their diameter. With object glasses, on the other 
hand, bending of the lens by its own weight in different positions has 
not been found to aflect appreciably the character of images formed by 
any of the great glasses, except the 40-inch, which suflers a slight de- 
formation of images in certain positions. Still, it must be remembered 
that the objective, although called achromatic, is not completely so ; 
and in some of the very large refractors, the intense blue light sur- 
rounding a bright object is often a serious obstacle in the work of 
practical observation. On the whole, the refractor is generally pre- 
ferred to the reflector. It is easier to adjust and keep in order ; and 
its tube being closed, it is much less subject to harmful effect of local 
air currents. It is a fact, too, that more than three fourths of all the 
work of astronomical observation has been done with refracting 
telescopes. 




Path of Rays through a Negative (Huygenian) Eyepiece 

The Eyepiece. — The eyepiece of a telescope is simply a magnify- 
ing glass, or microscope for examining the image of an object formed 
at the focus by the objective. Any small, convex lens, then, may 
be used as an eyepiece, but its effective field of view is very limited. 



The Eyepiece 



207 



So a combination of two plano-convex lenses is usually employed, in 
order that the field may be enlarged, and vision be distinct everywhere 
in that field. Two forms of celestial eyepiece are common, called the 
negative and the positive eyepiece. Both forms have a smaller, or 
eye lens, and a larger, or field lens ; the latter toward the objective, 
the former nearer the eye. In the negative (sometimes called from 
Huygens, its inventor, the Huygenian) eyepiece, both eye lens and 
field lens have their flat faces turned toward the eve, as in the 




Path of Rays through a Positive (,Ramsden> Eyepiece 

preceding figure. In the positive (called, also, from its inventor the 
Ramsden) eyepiece, the convex faces of both lenses are turned inward, 
or toward each other, as in the above figure, where the eye lens is drawn 
double its proper diameter. The negative eyepiece has its focus be- 
tween the two lenses. The focus of the positive eyepiece lies beyond 
both lenses, a short distance toward the objective. Positive eyepieces 
are always used for transit instruments and micrometers. Both these 
forms of eyepiece do not themselves invert, but when employed in con- 
junction with an object glass, they show all objects inverted, the objective 




Path of Rays through a Terrestrial or Erecting Eyepiece 

itself causing the inversion, because the rays cross in passing through it. 
A terrestrial or day eyepiece is one which, when employed with an object 
glass, shows all objects right side up. The re-inversion of the image 
necessary to effect this is produced, as shown in the preceding illustra- 
tion, by constructing the eyepiece of four lenses instead of two. Dif- 
ferent eyepieces of different magnifying powers may generally be used 
with the same objective, by means of suitable draw-tubes, called 
adapters. The same eyepiece can be used in either reflectors or refrac- 
tors. 



2o8 The Observatory and its Instruments 

To ascertain the Magnifying Power. — Following is an easy method : 
Select a convenient object marked with dividing lines at pretty regular 
intervals — clapboards on a house, bricks in a wall, or better the joints 
where plates of tin are lapped on a roof. When the sun is shining 
obliquely across them, set up the telescope as distant as possible, yet 
near enough so that the joints can readily be counted with the naked 
eye. Then point the telescope at the roof. Look at it through the 
eyepiece with one eye, and with the other look along the outside of 
the telescope at the roof also ; first with one eye, then with the other, 
then with both together. Amplification, or magnifying power (at that 
distance of the telescope from the roof) is equal to the degree of this 
enlargement ; and it can be ascertained by simply counting the number 
of divisions (as seen by the naked eye) w^hich are embraced between 
any two adjacent joints as seen in the telescope. The two images 
of the same object wnll be seen superposed, and a little practice will 
enable one to make the count with all necessary accuracy. Good tele- 
scopes are usually provided with an assortment of eyepieces whose magni- 
fying powers range approximately betw^een seven and 70 for each inch of 
aperture of the object glass. For example, a four-inch telescope would 
have perhaps four eyepieces, magnifying about 25, 90, 200, and 300 times. 

How to measure Small Angles. — The micrometer is an instrument 
for measuring small angles. It is attached to the telescope in place of 




A Modern Micrometer with Electric Illumination (Ellery) 

the eyepiece. The illustration show^s all the important working parts. 
Crossing the oblong field of view are seen two spider lines {aa)^ with 
which the measuring is done. All parts of the micrometer are so de- 
vised and related that these two lines can be seen at night in the 
dark field of view ; moved with accuracy slowly toward or from each 
other; and their exact position recorded. In the best modern microm- 
eters, either the lines or the field of view can be illuminated at will by 
a small incandescent electric lamp (Z). The spider lines are attached 
to separate sliding frames ; each frame can be moved by a thumb- 



The Trmisit InstrMmeut 



209 



screw, the head of which projects outside the micrometer box. One 
of these, called the micrometer screw, has enlarged heads (/^V/-) 
graduated to show the number of turns and fraction of a turn of this 
screw. The eyepiece (not shown) is a positive one attached to the 




A Compact Modern Transit Instrument (from a Design by Heyde) 

micrometer box in front of the sliding frames. To measure a small arc, — 
for example, the diameter of a planet — point the telescope so that the 
disk of the planet appears in the center of the field of view. Then turn 
the two thumbscrews until the spider lines are both seen tangent to 
opposite sides of the disk at the same time. Read the micrometer-head. 
todd's astron. — 14 



2IO The Observatory and its Instruments 



Then turn the micrometer-screw, until the two hnes appear as one. 
Read the head again ; take the difference of readings, and multiply it 
by the arc-value of one turn (which must have been previously deter- 
mined). Resulting is the diameter of the planet in arc. 

The Transit Instrument. — Soon after the invention of the telescope, 
early in the 17th century, an instrument was devised by a Danish 

astronomer, Roemer, which has now sup- 
planted nearly every other for determining 
time with precision. It is called the 
transit instrument, because used in observ- 
ing the passage, or transit, of heavenly 
bodies across the field of view^ Ordinarily 
it is mounted in a north and south line. 
On top of the two rigid triangular piers 
(preceding page) are bearings in which the 
axis of the transit instrument turns. The 
telescope F is secured at right angles to 
the axis C When turned round in its 
bearings, the telescope describes the plane of the meridian. On that 
account it is sometimes called a meridian transit. In the convenient 
type of transit here pictured, the axis forms half of the telescope tube. 
A glass prism in the central cube reflects the rays through C to the eye 
at the left. Such an instrument is often called a ^broken transit.' 
Until the instrument is reversed, the eye remains stationary, no matter 
what the declination of the star observed. 

Observing with the Transit Instrument. — First, it must be adjusted. 
A level, Z, hanging below^, makes the axis horizontal. In the field of 
view is a reticle, often made of spider lines, but sometimes by ruhng 
very fine lines with a diamond point on a thin plate of optical glass. 




Adjustable Reticle 




MATION 



EYEPIECE 



RETICLE OBJECT GLASS 

To show the Line of Collimation 



The reticle is accurately adjusted in focal plane of object glass, and in 
smaller instruments, surveyor's transits, for example, lines are arranged 
as in the two illustrations above. The lines are often called threads 
or wires. The line of collijjiation is the line from the center of object 
glass to the central intersection of lines of reticle. This line is ad- 
justed perpendicular to the axis of revolution of the telescope. Then by 
repeated trials upon stars, the Y's, or bearings, are shifted very slightly 
north or south, on pivots (page 209) under the left-hand end of the 



The Astrono77tical Clock 



21 I 



Reticle of Transit 



base, until the axis lies precisely east and west. When the foregoing 

adjustments have been made, the telescope, or more accurately the hne 

of collimation, swings round in the true plane of the meridian. To 

observe a star, count the beats of the clock 

while looking in the field of view ; and set 

down the second and tenth of its crossing 

the central vertical line of the reticle. In the 

illustration a star is seen approaching the 

vertical or transit lines. If a very accurate 

value is desired, observe the passage over 

the five central lines, and then take the 

average. This will be the time required. 

The Astronomical Clock. — Timepieces used in observatories are of 
two kinds, clocks and chronometers. One or the other is indispensable. 
The astronomical clock has a pendulum oscillating once each second : 
if it oscillates once a sidereal second, it is a sidereal clock ; if once a 
mean solar second, it is a mean time clock. A seconds hand records 
each oscillation. Also it has hour and minute hands, like ordinary 

clocks, except that the dial is 
usually divided into 24 hours 
instead of 12, for the conven- 
ience of the astronomer, in 
recording hours of the astro- 
nomical day, or in following the 
stars according to right ascen- 
sion. If, at any instant, the 
clock does not show exact 
time, the difference between 
true time and clock time is 
called the correction, or error 
of the clock. This must be 
found from day to day, or from 
night to night, by observing 
transits of the heavenly bodies 
with the meridian circle or the 
transit instrument. If a clock 
does not keep exact pace with 
the objects of the sky, it is 
said to have a rate. As with the chronometer, daily rate is the amount 
by which the error changes in 24 hours. A large rate is inconvenient, 
but does not necessarily imply a bad clock. The less the rate changes 
the better the clock. Dampness of the air and sudden changes of 
temperature are hostile to the fine performance of timekeepers of 
every sort. Equality of surrounding conditions is secured as much 




View into Clock-room (Lick Observatory) 



2 1 2 The Observatory and its Instruments 



as possible by keeping clocks and chronometers, as the last illustration 
shows, in a small and separate room, where the air may readily be kept 
dry arid its temperature nearly constant. 

Pendulum and Escapement. — Horology is the science which em- 
braces everything pertaining to measurement of time, and to mechani- 
cal contrivances for effecting this end. The chronometer is described 
and pictured in the preceding chapter (page 171). Accurate running of 
a clock is dependent mainly upon two parts of its mechanism, (a) the 

pendulum, and {b) the escape- 
ment. The pendulums of all 
observatory and standard 
clocks are compensated for 
temperature, so that the 
natural fluctuations of this 
element may have little or no 
effect upon the length of the 
pendulum, and therefore upon 
its period of oscillation. 
There is a variety of methods 
by which the compensation 
is effected. The illustration 
shows the simplest of them. 
The steel pendulum rod 
passes through a zinc tube 
(shaded), to the bottom of 
which is attached the heavy 
pendulum-bob. With a rise 
of temperature, the down- 
ward expansion of the steel 
is just equalized by the up- 
ward expansion of the zinc ; 
so the center of oscillation 
remains at the same distance 
from the point of support. 
The center of oscillation is 
that point of a pendulum in which, if the whole mass of the pendulum 
were concentrated, the period of oscillation would not vary. The grid- 
iron pendulum and the mercurial pendulum are other forms of compen- 
sation. Next in importance to the pendulum is the escapement. The 
illustration represents in outline one of the best forms. It is called 
the gravity escapement, because the pendulum is driven by the pressure 
alternately of two gravity arms, which are swung aside by the six black 
pins in the hub of the escapement wheel. The clock train does the 
work of raising the arms outward from the pendulum rod ; so that the 




Compensation 
Pendulum 



Gravity Escapement 



The Chronograph 



213 



pendulum swings almost perfectly free, having no work to do except 
to raise the gravity arms just enough to trip the escapement at the 
smoothly polished jewels AA. 

The Chronograph. — In recording transits of the heavenly bodies, 
greater convenience, rapidity, and precision are attained by using the 
chronograph, a mechanical contrivance first devised by American 
astronomers about 1850, and now used in observatories universally. 
The illustration shows an excellent type of this instrument. The 
chronograph consists of a cylinder about 8 inches in diameter and 




A Modern Chronograph by Warner & Swasey 

16 inches in length, which revolves once every minute at a uniform 
speed. Wound upon it is a sheet of blank paper, and above it trails 
a pen connected with an armature, so that every vibration of the pen- 
dulum, by closing an electric circuit, joggles the pen or throws it aside a 
fraction of an inch at the beginning of each second. The illustration 
(next page) shows a small part of a chronograph sheet, full size. As 
the barrel or cylinder revolves, the pen carriage travels slowly along, so 
that the trail of the pen is a continuous spiral round the barrel, with 
60 notches or breaks in every revolution. In the circuit of the pen 
armature is a small push button, called an observing key. This is held 
in the hand of the observer while the star is passing the field. When- 
ever it crosses a spider line, a tap of the observing key records the 
instant automatically on the chronograph paper, which may be removed 
and read at leisure. As is apparent from the illustration, tenths of a 
second are readily estimated, even without any measuring scale. The 
breaks at regular intervals are made automatically by the timepiece. 
The short breaks between A and B are made in quick succession by 



214 ^/^^ Observatory and its Instruments 



[h 



? P r"/^-^ 



6' 



I a 



3' 



Part of the 

Chronograph 

Sheet 



the observer, to show that a star is just coming to the 
lines. Transit of the star over the first two lines took 
place at C (7 h. i6 m. 7.4 s.), and at D (7 h. 16 m. 1 1.4 s.), 
reading in all cases from the preceding (or lower) side of 
the break. By transits of ten stars of five lines each, a 
good observer can determine the error of his timepiece 
within two or three hundredths of a second. Hough has 
recently perfected a printing chronograph which records 
the time in figures on a paper fillet. 

Personal Equation. — Few observers, no matter how 
practiced, tap the key exactly wiien a star is crossing a 
line. Most of them make the record just after the star 
has crossed, and still others always press the button a 
small fraction of a second before the star reaches the 
wire. It does not matter how much too early or too late 
the record is made, because the difference can usually be 
found by methods known to the practical astronomer ; 
but a good observer is one who makes this difference 
invariable ; that is, his personal equation should be a con- 
stant quantity. The personal equation of an observer 
is the difference betw^een his record of any phenomenon, 
and the thing itself. In observing transits of heavenly 
bodies, most observers have a personal equation amount- 
ing to one or two tenths of a second of time. Personal 
equation is usually found by observing with a personal 
equation machine, an instn,unent which records on a 
single chronograph sheet, not only the observer's time of 
transit, but also the absolute instant w^hen the star is 
crossing the lines. The next illustration shows such a 
machine. Light from the lamp on the right provides an 
artificial star which the clockwork makes to travel across 
the lines in front of the observing tube on the left. Abso- 
lute time is time corrected for personal equation. It is 
nearly always required in the accurate determination of 
longitudes by the electric telegraph. 

The Photo-chronograph. — As the effect of personality 
is usually absent from all records made by photography, 
many attempts have been made to register star-transits 
by photographic means. The instrument which does this 
takes the place of both eyepiece and chronograph, and 
is called the photo-chronograph. Opposite is a picture 
of this ingenious little instrument. If a photographic 
plate is firmly fixed in the focal plane of a transit instru- 
ment, and a star is allowed to move through the field, the 



The F koio-clu^onograph 



215 




Machine for determining Personal Equation (Eastman) 



negative will show a fine, dark line or trail, crossing the plate hori- 
zontally from west to east. By holding a lantern in front of the object 
glass a few seconds, the ver- 
tical lines in the field may 
also be obtained on the same 
plate. There will be, then, 
an absolute record of the 
star's path through the field 
and across the hnes ; but 
nothing will be known as to 
the time when the star was 
crossing any particular line. 
Now instead of fastening the 
plate, insert it in a little 
frame which slides north and 
south a small fraction of an 
inch. So arrange the details 
of the mechanism that an 
armature will move the frame 
automatically. Connect this 
armature into a suitable clock 
circuit, in place of the ordi- 
nary chronograph pen. In- The Photo-chronograph (Fargis-Saegnaiiller) 




2 1 6 The Observatory and its Instruments 

stead of a star transit, or ordinary, horizontal trail like this — 



Ordinary Star Trail 

the plate when developed will show this — 



Interrupted Star Trail 

It is easy to find the particular second corresponding to each one 
of the little broken trails on the plate, and by using a magnifying 
glass the fractional parts of seconds where the reticle lines cross the 
trails can be measured with accuracy and with almost no effect of per- 
sonal equation. In another form of photo-chronograph, the plate is 
stationary, and the armature actuates an occulting bar, which screens 
the plate except for an instant at the end of each second. The star 
trail is then reduced to a series of equidistant dots. 

The Meridian Circle. — The meridian circle is an instrument for 
measuring right ascensions and declinations of heavenly bodies. Its 

foundations are two piers or 
pillars, in an east and west line. 
On top of each is a Y? or bear- 
ing, and in these turn two 
pivots, accurately fashioned, 
cylindrical in form. On top of 
them rests an accurate striding 
level. The pivots are attached 
solidly to the massive axis 
proper, this latter being made 
up of two cylinders, or in- 
verted cones, and a central 
cube between them, through 
which passes the telescope, 
rigidly fastened perpendicular 
to axis. On either side of 
the telescope, a finely divided circle is secured at right angles to the 
axis. Circles, axis, telescope, and pivots, then, all revolve round in the 



LAMP 

lUUMINATmOy 

fi£.TICLC 




Meridian Circle ;from a Design by Landreth) 



The Equatorial Coude 2 1 7 

Y's together, as one solid piece. The deHcate bearings are in part re- 
lieved of this great weight by means of counterpoises, f^irmly attached 
to the right pier are microscopes for reading with high accuracy the 
graduation on the rim of the circle. The zero point of the circle is 
usually found by placing a basin of mercury underneath the telescope, 
which is then pointed downward upon the mercury. When the hori- 
zontal lines in the field of view are seen to correspond exactly with 
their images reflected from the mercury, the position of the circle is read 
from the microscopes ; and this is the zero point, because the line of 
sight through the telescope is then vertical. The operation of obtain- 
ing this zero point is called * taking a nadir.' Combining it wdth the 
latitude of the place gives the circle reading for pole or equator, and 
so any star's declination may be found. The meridian circle is often 
called also the transit circle. Right ascensions are observed with 
the meridian circle exactly as with the transit instrument previously 
described. 

The Equatorial Coude. — A very advantageous and convenient combi- 
nation of refractor and reflector is the T-shaped or • elbow telescope." 
called the equatorial coude. It was invented by Loewy, the present 
director of the Paris Observatory, and is a type of instrument well known 
in the observatories of France, 
although there are as yet none ^^^^ 

in the United States. The v ':^. 

chief advantage is that the 
instrument itself, as show^n in 
the illustration, is nearly all 
in open air, while the observer , 
sits in a fixed position, as if 

working at a microscope on The Equatorial Coude iLoewy) 

a table. The eyepiece, there- 
fore, -is in a room which may be kept at comfortable temperatures 
in winter. The instrument can be handled easily and rapidly, and is 
very convenient for the attachment of spectroscopes and cameras. The 
splendid lunar photographs on pages i6 and 248 were taken with this 
telescope. Its chief disadvantage is loss of light by reflection from 
two plane mirrors, set at an angle of 45° in two cubes shown at the 
lower end of the polar axis. The object glass is mounted in one 
side of the right-hand cube, near the attendant. This cube with its 
mirror and objective turns round on an axis in line with the central 
cube, and forming the declination axis. Beneath the central cube is 
the low-er pivot of the polar axis. The long oblique- telescope tube is 
itself the polar axis, and its upper bearing is near the eyepiece. A 
powerful clock carries the whole instrument round to follow the stars, 
and the upper cube is counterpoised by a massive round weight at the 




2i8 The Observatory and its Instruments 

lower end of the declination axis. First cost of the equatorial coude 
is about double that of the usual type of equatorially mounted telescope ; 
but the large expense for a dome is mostly saved, as the coude is 
housed under a light structure which rolls off on rails to the position 
shown in the engraving. 

Common Mistakes about Telescopes. — Perhaps the question most 
often asked the astronomer by persons uninformed is, How far can you 
see with your telescope ? Evidently no satisfactory answer can be given, 
for all depends upon what one wants to see. If terrestrial distance is 
meant, the large telescope does not possess an advantage proportionate 
to its size. All objects on the earth must be observed through lower 
strata of the atmosphere, and these regions are so much disturbed in 
the daytime by intermingling of air currents, warm and cold, that 
the high magnifying powers of large telescopes cannot be advanta- 
geously used. If celestial distance is meant by the question, How far.^ 
the answer can only be inconclusive, because the telescope enables us 
to see as far as starlight can travel. The brighter the star, the greater 
distance it can be seen, independently of the telescope. The smallest 
glass will show stars so far away that light requires hundreds of years 
to reach us from them. The larger the telescope, the fainter the star it 
will show ; but it is not known whether these fainter stars are fainter 
because of their greater distance or simply because they are smaller or 
less luminous. Another common question is. How much does your 
telescope magnify? as if it had but one eyepiece. Actually it will have 
several, for use according to the condition of the atmosphere and the 
character of the object. A more intelligent question would be, What is 
the highest magnifying power? This will never exceed loo diameters 
to each inch of aperture of the objective, and 70 to the inch is an 
average maximum. Even this, however, is high, if advantageous 
magnifying power is meant. So unsteady is the atmosphere in the 
eastern half of the United States that magnifying powers exceeding 
50 to the inch cannot often be used to advantage in observing the 
planets. 

Celestial Photography. — As soon as Daguerre, in 1839, had invented 
photography, it was at once seen that the brighter heavenly bodies 
might be photographed, because telescopes are used to form images 
of them in exactly the same way that the camera produces an image of 
a person, a building, or a landscape. Photography is simply a process 
of fixing the image. In 1840 the moon was first photographed, in 1850 
a star, in 1851 the sun's corona, in 1854 a solar eclipse, in 1872 the 
spectrum of a star, in 1880 a nebula, in 1881 a comet, and in 1891 a 
meteor. All these photographs, except the meteor and the corona, were 
first made in America. Continued improvement in processes of photog- 
raphy makes it possible to take pictures of fainter and fainter celestial 



Photographs of the Heavenly Bodies 219 

bodies, and the larger telescopes have photographed exceedingly faint 
stars which the human eye has never seen — perhaps never can see. 
This is done by exposing the sensitive plate for many hours to the 
light of such bodies ; for, while in about 10 seconds the human eye, 
by intense looking, becomes weary, the action of faint rays of light 
upon the photographic plate is cumulative, so that the result of several 
hours' exposure is rendered readily visible when the plate is devel- 
oped. In this way, an extra sensitive dry plate, of the sort most generally 
employed, will often record many thousand telescopic stars in a region 
of sky where the naked eye can see but one (page 458). Nearly every 
branch of astronomical research has been advanced by the aid of pho- 
tography, so universal are its applications to astronomy. 

How to take Photographs of the Heavenly Bodies. — Any good tele- 
scope or camera may be satisfactorily used in taking photographs of 
celestial objects. Remove the eyepiece, and substitute in its place a 
small, light-tight plate-holder. Fasten it to the tube temporarily, so 
that the plate will be in the focus of the object glass. This point may 
be found by moving forth and back a piece of greased or paraffin paper, 
until the image of the moon is seen sharply defined. Adjust plate- 
holder and finder so that when an object is in the field of the finder, 
it will also be on the center of the plate. Insert a plate in this position, 
and make an exposure of about half a second on the moon, if within 
two or three days of the ^ quarter.' The object glass should be covered 
by a cap or diaphragm having about three fifths the full aperture of the 
lens. On developing, the moon's image will be somewhat blurred. In 
part this is because the best focus for photographing is either outside or 
inside the visual focus, found by the greased paper. To find the best 
focus, move the plate-holder farther from the lens, first \ inch, then \ 
inch, then | inch, then i inch, making at each point an exposure of 
the same length as before. Compare the negatives. The true photo- 
graphic focus lies nearest the point where the best-defined picture was 
taken. If desired, the process may be repeated near this point, shift- 
ing the plate only a few hundredths of an inch each time. If the 
pictures are more and more blurred the farther the plate is moved from 
the lens, the focus for photography may be inside the visual focus 
first found, and the plate-holder should then be moved in accordingly, 
making trials at different points. When the photographic focus is 
finally found, the plate-holder should be securely fastened to the eye- 
piece tube, or adapter ; and a mark made so that it may readily be 
adjusted to the same spot whenever needed in the future. A meniscus 
of suitable curvature is sometimes attached in front of the object glass, 
to focus the photographic rays (about I nearer the objective). Also 
E.G. Pickering has found that an achromatic objective with crown lens 
properly figured can be converted into a photographic telescope by 



2 20 The Observatory and its Instrtiments 

reversal of the crown lens. In achromatic objectives of the new Jena 
glass, visual and photographic foci are practically coincident. 

Astronomical Discoveries made by Photography. — The great benefit 
to astronomy from the application of photography in making discoveries 
was first realized when, during the total eclipse of 1882 in Egypt, the 
photographic plate discerned a comet close to the sun (page 301). But 
interest was intensified when a hazy mass of light was seen to surround 
the star Maia of the Pleiades, on a plate exposed for about an hour to 
that group of stars in November, 1885. This astronomical discovery 
by means of photography was soon after verified by the 30-inch tele- 
scope at Pulkowa. Russia. IMany other nebula, both large and small, 
have since been discovered by photography, some of which have been 
verified by the eye. By photographing spectra of stars, peculiarities of 
constitution have been immediately revealed which the eye had long 
failed to discover directly (page 444) . Several new double stars have 
. been found in this way, and important discoveries as to classification 
of stars have been made from critical study of stellar spectrum photo- 
graphs (page 444). Long exposures of comets have brought to light 
certain details of structure which the eye has failed to detect (page 
406). In discovering minor planets, photography has. since 1890, been 
of constant assistance because of ease and accuracy in mapping fixed 
stars in the neighborhood of these minute objects. It is about 20 times 
easier to find a small planet on a photographic plate than by the former 
method of mapping the sky optically. But discoveries in solar physics 
by means of photography are most important of all, for it has been 
found that the faculae. or white spots, extend all the way across the sun's 
disk in about the same zones that spots do (page 269) : and complete 
photographic records of the sun's chromosphere and prominences are 
now made every day by means of radiations to w4iich photographic 
plates are very sensitive, but which our eyes unaided are powerless to 
see. Lunar photographs, too. are thought by some astronomers to have 
revealed minute details which the eye has failed to detect. 

We now turn to a consideration of present knowledge of 
our satellite, and of the other and more remote orbs of 
heaven, as disclosed by the instruments of which we have 
just learned. 



CHAPTER X 

THE MOON 

THE moon was the subject of the most ancient astro- 
nomical observations, for elementary study of her 
motion was found both easy and useful. The wax- 
ing and waning phases, too, must have excited the curi- 
osity of early peoples, who were unacquainted with the 
true explanation of even so elemental a phenomenon. Let 
us now watch our satellite from night to night. A few 
evenings' observations show how easy it is to find out the 
general facts of her motion around us. 

To observe the Moon^s Motion. — The September new moon, first 
becoming visible in the southwest, will, in about five days, reach the 
farthest declination south, and culminate near the lowest point on the 
meridian. Thenceforward, for about a fortnight, she will be farther and 
farther north each night, journeying at the same time eastward, and in 
a general way following the ecliptic. During the subsequent fortnight, 
the moon will be traveling southward, always within the zodiac ; and 
in a little less than a month, will have returned very nearly to the 
point where we first began to observe. And so on, throughout all 
time, with a regularity which became useful to the ancients as a meas- 
ure of time ; for our month took its origin from the moon^s period round 
the earth. But her motion is even more useful to the modern world, 
because employed by navigators on long voyages in finding the position 
of ships. So important is the moon in this relation that the lives of 
many great mathematical astronomers have been almost wholly devoted 
to the study of her motion. Americans prominent in this hne of re- 
search are Newcomb and G. W. Hill. As soon as the new moon can 
first be seen in the western sky, make a long, narrow chart of the 
brighter stars to the east within the zodiac as on the next page. A line 
drawn eastward from the moon, perpendicular to the line joining the 

221 



222 



The Moon 



horns of the crescent, called cusps, will show this direction accurately 

enough. Then plot the moon among the stars on the chart each clear 

^ night. Also draw the phase as 

• • ^ • . ^ accurately as possible. It is bet- 

NEw MOON ^J ^ ter to chart the position about half 

/ . an hour later each night. This 

simple series of observations may 
continue nearly three weeks, if 
desired. Much will be learned 
from it. — position of the ecliptic ; 
progressive phases of the moon ; 
the amount of motion each day 
(about her own breadth every 
hour, or 13° in a day) ; and if a 
telescope is used, the observer will 
occasionally be rewarded by the 
opportunity of watching the moon 
pass over, or occult, a star. Dis- 
appearance of a star at the moon's 
dark limb is the most nearly in- 
stantaneous of all natural phe- 
nomena. 



V 



V 



NEW CRESCENT I 
MOON ^ 



FIRST QUARTER | 



GIBBOUS MOON 
BEFORE FULL 



o 



-^ £ 



GIBBOUS MOON 
AFTER FULL 



THIRD OR LAST , 
QUARTER ' 



OLD CRESCENT I 
MOON ^ 



-§^ I 



-^ i 



111' 



The Terminator. — Ob- 
serve the slender moon in 
the west, as soon as she can 
be seen in a dark sky. The 
inside edge of the bright 
crescent, or the Hne where 
the lucid part of the moon 
joins on the dark or faintly- 
illuminated portion, is called 
the terminator; and its gen- 
eral curvature is always a 
half ellipse, never a semi- 
circle. 

The moon's terminator is ellip- 
tical in figure because it is a semi- 
circle seen obliquely. Any circle 
not seen perpendicularly seems to 



The Moons Phases 



223 



be shaped like an ellipse ; and the more obliquely it is seen, the more 
the ellipse appears elongate or drawn out. When turning a curve on 
your bicycle, observe the changing figure of the shadows of its wheels 
cast by the sun. Owing to mountains on the lunar surface, the actual 
terminator, if examined with a telescope, is always a broken, jagged 
Hne. This is because sunlight falls obhquely across the rough surface, 
and all its irregularities are accentuated as if magnified — like pebbles 
and ruts in the road, at a considerable distance from an arc light. 




© FULL ©^ 

MOON 
Phases as seen from above Moon's Orbit 



O 



FULL 

o 

MOON 



o 



/ 



Corresponding Phases from the Earth 



Explaining Phases of the Moon 

The Moon's Phases. — The moon's phases afforded trav- 
elers and shepherds the first measure of time. When two 
or three days after new moon our satelhte is first seen in 
the western sky, her form is a crescent, convex westward 
or toward the sun, with the horns, or cusps turned toward 
the east. Three or four days later the slender crescent 
having grown thicker and thicker, and the terminator less 
and less curved, the moon has reached quadrature, or first 
quarter, and her shape is that of a half circle. The termi- 
nator is then a straight line, the diameter of this circle. 
Passing beyond quadrature, the terminator begins to curve 



2 24 The Moon 

in the opposite direction, making the moon appear shaped 
somewhat like a football, with one side circular and the 
other elliptical. The eastern edge is the elliptical one, 
and is still called the terminator. Gradually its curva- 
ture increases, the apparent disk of the moon growing 
larger and larger, until, about a week after first quarter, 
the phase called full moon is reached. This oblong 
moon, between first quarter and full, is called gibbous 
moon. From full moon onward for a week, our satellite 
is again gibbous in form, but the terminator has now 
changed to the west side of the lunar disk, instead of 
the eastern. Then quadrature is reached, and the moon 
is again a half circle, but turned toward the east, not the 
west. This phase is known as third, or last quarter. On- 
ward another week to new moon, the figure is again cres- 
cent, but curving eastward or toward the sun, and the 
horns pointing toward the west. All the figures previously 
shown — crescent, quarter, gibbous, and full — represent 
phases of the moon. 

Cause of the Moon's Phases- — Our satellite is herself a 
dark, opaque body. But the half turned toward the sun is 
always bright, as in the last figure ; the opposite half is 
unillumined, and therefore usually invisible. While the 
moon is going once completely round the earth, different 
regions of this illuminated half of our satellite are turned 
toward us ; and this is the cause of phases of the moon. 

To illustrate in simple fashion : accurately remove the peel from the 
half of an orange. Let a lamp in one corner of a room otherwise dark 
represent the sun. Standing as far as convenient from the lamp, let 
the head represent the earth, and the orange held at arm's length, 
the moon. Turn the white half of the orange toward the lamp. Now 
turn slowly round toward the left, at the same time turning the orange 
on its vertical axis, being careful ahvays to keep the peeled side of the 
orange squarely facing the lamp. While turning round, keep the eye 
constantly fixed on the white half of the orange, and its changing 



Earth Shine 



225 



shape will represent all the moon's successive phases : new moon w^hen 
orange is between eye and lamp ; first quarter (half moon) when orange 
is at the left of lamp and 
at a right angle from it ; 
full moon when orange is 
directly opposite lamp ; 
last quarter, orange oppo- 
site its position at first 
quarter. When the orange 
shows a slender crescent, 
at either old or new moon, 
shield the eye from direct 
light of lamp. Again re- 
peat the experiment, and 
watch the gradually curv- 
ing terminator from phase 
to phase. The impeded 
half of the orange, too, 
represents very well the 
moon's ashy light, or 
earth shine on the moon, 
when a narrow crescent. 

Earth Shine. — The 

nights on the moon 
are brightened by re- 
flected Kght from the 
neighborly earth, and 
our shining is equal to more than a dozen full moons. 
This light it is that makes the faint appearance on the 
moon, as of a dark globe filling the slender crescent of the 
new moon, causing a phenomenon called ' the old moon 
in the new moon's arms.' Similarly with the decrescent 
old moon. 

The copper color of the earth-illumined portion is explained by the 
fact that the earth light has passed twice through our atmosphere before 
reaching the m.oon, and by a peculiar property of the atmosphere, it 
absorbs bluish rays and allow's reddish ones to pass. Always the 
phase of this portion of the moon is the supplement of the phase of the 
bright portion. Also its figure is exactly that w^hich the bright earth 
todd's astron. — 15 




Illustrating the Moon's Progressive Phases 



2 26 The Moon 

would appear to have, if seen from the moon. When our satellite is 
crescent or decrescent to us, the earth shows gibbous to the moon. 

North and South Motion of the Moon. — Just as the sun 
has a north and south motion in a period of a year, so the 
moon has a similar motion in a period of about a month ; 
for she follows in a general way the direction of the ecliptic. 
Every one has observed that midsummer full moons always 
cross the meridian low down, and that the full moons of 
midwinter always culminate high. 

The reason is that the full moon is always about i8o degrees from 
the sun. Similarly midwinter crescent moons, whether old or new, are 
always low on the meridian, and crescent moons of midsummer always 
high. So when in summer you see in early evening the new moon in 
the northwest, you know that in winter the old moon's slender crescent 
must be looked for in the early morning in the southeast. Remember 
that our satellite from new to full is always east of the sun. And 
whether the moon in this part of its lunation is to be found north or 
south of the sun will depend upon the season. For example, the moon 
at first quarter will run highest in March, because the sun is then at the 
vernal equinox, and the moon at the summer solstice. For a like reason 
the first-quarter moon which runs lowest on the meridian will "full' in 
the month of September. 

The Moon rises about Fifty Minutes later Each Day. — 

Her own motion eastward among the stars, about 13° every 
day, causes this delay. As our ordinary time is derived 
from the sun (itself not stationary among the stars, but 
also moving eastward every day about twice its own 
breadth, or 1°), therefore the eastward gain of the moon 
on the sun is about 12°. Now suppose the moon on 
the eastern horizon at 7 o'clock this evening ; then, to- 
morrow evening at 7, it is clear that if her orbit stood ver- 
tical, she would be 12° below the horizon, because in that 
part of the sky the direction east is downward. But by 
the earth's turning round on its axis, the stars come above 
the eastern horizon at the rate of 1° in four minutes of 
time ; therefore to-morrow evening the moon will rise at 



Harvest and Hunters Moon 227 

about 50 minutes after 7. And so on, about 50 minutes 
later on the average each night. 

Variation from Night to Night. — Consult the almanac 
again. In it are printed the times of moonrise for every 
day. Wait until full moon, and verify these times for a 
few successive days, if the eastern horizon permits an un- 
obstructed view. Having found the almanac reliable, at 
least within the limits of error of observation, we may use 
its calculations to advantage for other days of the year ; 
for on many of these it will not be possible to watch 
the moon come up, because she rises in the daytime. The 
difference of rising (or of setting) from one day to another 
may sometimes be less than half an hour, and again about 
a fortnight later, a full hour and a quarter. 

There are two reasons for this: (i) The apparent monthly path of 
the moon lies at an angle. to the horizon which is continually changing; 
when the angle is greatest, near the autumnal equinox, a day's east- 
ward motion of our satellite will evidently carry her farthest below the 
eastern horizon. (2) The moon's path around us is elliptical, not circu- 
lar, and the earth is not at the center of the ellipse, but at its focus, 
so that earth and moon are nearest together and farthest apart alter- 
nately at intervals of about two weeks. By the laws of motion in such 
an orbit, the moon travels her greatest distance eastward in a day 
when nearest the earth (perigee) ; and her least distance eastward when 
farthest from the earth (apogee) . And this change in speed of the 
moon's motion also affects the time of rising and setting. 

Harvest and Hunter's Moon. — Every month the moon 
goes through all the changes in the amount of delay in her 
rising, from the smallest to the largest. But ordinarily 
these are not taken especial account of, unless at the time 
when least retardation happens to coincide nearly with 
time of full moon. Now the epoch of least retardation 
occurs when the moon is near the vernal equinox, be- 
cause there the moon's path makes the smallest angle with 
the eastern horizon. And as sun and full moon must be 



228 The Moon 

in opposite parts of the sky, autumn is the season when 
full moon and least retardations come together. 

The daily advance of the moon along the September ecliptic is from 
I to 2, and from 2 to 3. In March the same amount of eastward 
advance, from i to 2^, and from 2' to 3'', brings the moon much farther 
below the horizon, and therefore retards the time of rising by the greatest 
amount, as the dotted lines drawn parallel to the equator show. Simi- 
larly the positions at 2 and 3 give the least delay ; and this September 
full moon, rising less than a half hour later each evening, is called the 
harvest moon. A month later the retardation is still near its least 
amount for a like reason ; and the October fall moon is called the 
hunter's moon. Approaching the tropics, where equator and ecliptic 
stand more nearly vertical to the horizon, it is clear that the phe- 
nomena of the harvest moon become much less pronounced. 




/ 

Circumstances of Harvest Moon 



The Moon's Period of Revolution. — The moon revolves 
completely round the starry heavens in 2j\ days (or more 
exactly 27 d. /h. 43 m. 11.5 s.). This is called the sidereal 
period of the moon, because it is the time elapsed while she 
is traveling from a given star eastward round to the same 
star again. This motion of the moon must be kept en- 
tirely distinct from the apparent diurnal motion, or simple 
rising in the east and setting in the west ; for the latter 
is a motion of which all the stars partake, and is wholly 



The Moons Sy^iodic Period 



229 



due to the earth's revolution eastward- upon its axis. But 
our satellite's own motion along her path round the earth is 
in the opposite direction ; that is, from west toward east. 
A rough value for the sidereal period is easy to determine. 

Select any bright star (not a planet) near the moon ; for example, 
Alpha Scorpii, on 30th September, 1897, at about 7 p.m., Eastern 
Standard time. The star and the center of the moon are then nearly 
on the same hour circle ; that is, their right ascensions are about equal. 
The following month watch for the moon's return to the same star ; on 
the evening of 27th October, at 6 o'clock, the moon has not yet 
reached the star, but is about nine times her own breadth west of the 
star. So star and moon are together about three in the morning of 
28th October. The difference, then, or 27 d. 8h., although a crude 
verification of the sidereal period, has been rightly obtained. 

The Moon^s Synodic Period. — Let sun and moon appear together 
in the sky as seen from the earth at E^ sun being at S^ and moon at M^, 
While earth is trav- 
eling eastward round 
the sun in the direc- 
tion of the large ar- 
row, moon is all the 
time going round 
earth in the direc- 
tion M^M^ indicated 
by the small arrow. 
When earth has 
reached E , moon is 
at ///j, and her side- 
real period is then 
complete, because 
in^E is parallel to 
M^E. But the sun 
is in the direction 

E'S. So the moon must move on still further, making the period rela- 
tively to the sun longer than her sidereal period, just as the sidereal day 
is shorter than the solar day. In round numbers, the sun's apparent 
motion, while the moon has been traveling round us, amounts to about 
30°; therefore the moon must travel eastward by this amount, or nearly 
i\ days of her own motion, in order to overtake the sun. 

The period of the moon's motion round the earth rela- 
tively to the sun is called the synodic period. It is 2<^\ 




^f \ ^H 



Synodic Period exceeds Sidereal Period 



230 The Moo7i 

days in duration, or- accurately 29 d. 12 h. 44 m. 2.7 s., as 
found by astronomers from several thousand revolutions 
of the moon. It is an average or mean period, depending 
upon the mean motion of the sun and the mean motion of 
the moon ; for we shall soon find that our satellite travels 
round us with a speed far from uniform, just as we found 
our own motion round the sun to be variable. The synodic 
period may be roughly verified by observing the times of 
a given phase of the moon with about a year's interval 
between them, and dividing by the whole number of luna- 
tions. For example, on 2d October, 1897, at about nine in 
the evening, the terminator is judged to be straight, and it 
is first quarter. Similarly, on 22d September, 1898, at 6 
o'clock P.M. Divide the entire interval of 354.9 days by 
12, the number of intervening lunations, and the result is 
29.58 d., only one hour in error. 

The Lunation. — The term limation is often used with 
the same signification as the synodic period. More prop- 
erly the lunation is the period elapsing from one new 
moon to the next. Its value cannot be found directly by 
observation, but only from calculation, because at new 
moon the dark half of our satellite is turned toward us, 
and the disk is merged in the background of atmosphere 
strongly illuminated by the sun. Take from any almanac 
the difference between the times of adjacent new moons 
at different times of the year. Some of these will be 
longer and some shorter by several hours than the synodic 
period. These differences are mainly due to {a) the sun's 
varying motion along the ecliptic, and (b) the moon's 
varying motion in her path round the earth. 

The Moon's Apparent Orbit. — So far the moon's motion 
has been accurately enough described by saying that its 
path coincides with the ecliptic. But closer observation 
will soon show that, twice each month, our satellite deviates 



The Mooii s Apparent Orbit 



231 



from the ecliptic by 10 times her own breadth. This angle, 
more accurately 5° 8' 40^', is the inclination of the moon's 
orbit to the ecliptic, and it varies scarcely at all. Just as 
ecliptic and equator cross each other at two points 180° 
apart, called the equinoxes, so the moon's path and the 
ecliptic intersect at two opposite points, called nodes of 
the moon's orbit, or more simply the moon's nodes. 




Illustrating Inclination and Nodes of Lunar Orbit 

In the figure they are represented at a and b^ as coincident with the 
equinoxes, T and =2=. That, however, is their position for an instant 
only ; for they move constantly westward just as the equinoxes do, only 
very much more rapidly. During the time consumed by our satellite 
in traveling once around us, the moon's nodes travel backward more 
than twice the moon's breadth; so that in 181 years the nodes them- 
selves travel completely round the ecliptic, and return to their former 
position. When journeying from south to north of the ecliptic, as from 
d to c^ in the direction indicated by the arrow, the moon passes her 
ascending node, at a. And when going from c to d, she passes her 
descending node at b. When the inclination of the moon's orbit is 



232 



The Moon 



NEWAMOON 



added to the obliquity of the ecliptic, our satellite moves in the plane 
acbd, in the direction of the arrows ; when the inclination is subtracted, 
she moves in the plane agbf. In both cases the nodes coincide with the 
equinoxes : but in the latter the ascending node has moved round to b^ 
and the descending node to a. Extreme range of moon's declination 
is from 28''. 6 north to 28°. 6 south. 

Cardinal Points of the Moon's Orbit. — When our satel- 
lite comes between earth and sun, as at new moon, she is 
said to be in conjunction; at the oppo- 
site part of her orbit, with sun and moon 
on opposite sides of the earth, as at full 
moon, she is said to be in opposition. 
Both conjunction and opposition are 
often called syzygy. Halfway between 
the syzygies are the two points called 
quadrature. At quadrature the differ- 
ence of longitude between sun and moon 
is 90° ; at the syzygies, this difference is 
alternately 0° and 180°. The term syzygy 
is derived from the Greek word meaning 
a yoke, and is applied to these two rela- 
tions of sun, earth, and moon, when all 
these bodies are in line in space — or 
nearly so. 

True Shape of the Moon^s Orbit in Space. — If 

the earth did not move, the moon's orbit in space 
would be nearly circular. But during the month 
consumed by the moon in going once around us, 
we move eastward about jV of an entire circum- 
ference, or 30^. The moon's orbital motion is 
relatively slow, the earth's relatively rapid ; and 
on this account the moon winds in and out, along 
our yearly path round the sun. As that illumi- 
nating body is about 400 times more distant than the moon, the true 
shape of the lunar t)rbit cannot be shown in a diagram of reasonable 
size. But a small portion of the orbit can be satisfactorily shown, as 
above ; and it readily appears that the moon's real path in space is 
always concave to the sun. 



newv/moon 



Orbit Concave to Sun 
even at New Moon 



Distance of the Moon 233 

Form of the Moon's Orbit round the Earth. — In the 
case of sun and earth, we found that the shape of our 
yearly path round him is an elHpse, without knowing any- 
thing about our distance from him. In Hke manner we 
can find the form of the moon's monthly orbit round the 
earth. That also is an ellipse. 

By measuring the moon's diameter in all parts of her orbit, we shall 

find variations which can be due only to the changing distance of our 

satellite from us. The two circles adjacent 

correspond to extremes of this variation : the ^^^^TTT:::^^^ 

moon w^hen nearest to us, is said to be at /y'' ^'n\ 

perigee, and the outer circle represents its // \\ 

apparent size. About a fortnight later, on // \\ 

arrival at greatest distance, called apogee, the ; J 

moon's apparent size will have shrunk to the \\ / / 

inner dotted circle. Evidently the variation V\ // 

of apparent diameter is much greater than X^., _ ...--^/ 

that of the sun ; therefore the moon's path /^""""^ — 

is a more elono^ated ellipse than the earth's. /a'^^ 'f^^^+ j^I^- ?\ 

* . ^ . and Apogee (Dotted Circle) 

We saw that the eccentricity of the earth's 

orbit is -^^ : that of the moon's orbit is y^- So great is this variation 
in distance of our satellite that full moons occurring near perigee are 
noticeably brighter than those near apogee. While at new moon, as 
we shall see in Chapter xii, this change of the moon's apparent diam- 
eter happens to be very significant ; for it produces different types of 
eclipses of the sun. 

Distance of the Moon. — Of all celestial bodies, excepting 
meteors and an occasional comet, the nearest to us is the 
moon. Astronomically speaking, and relatively, the moon 
is very near, and yet her distance is too great to be appre- 
hended by reference to any terrestrial standard. As her 
orbit is elliptical instead of circular, and as the earth is 
situated in one of the foci of the ellipse, the average or 
mean distance of the moon's center from the center of our 
globe is 239,000 miles. 

If the New York-Chicago limited express could travel from the earth 
to the moon, and should start on New Year's, although it might run 



2 34 



The Moon 



day and night, it would not reach the moon till about the ist of Sep- 
tember. Recalling definitions of the ellipse previously given, it will be 
remembered that the mean distance is not the half sum of the greatest 
and least distances, but the mean of the distances at all points of the 
orbit. Also it is equal to half the major axis of the orbit. But in 
traveling round the earth, our satellite is not free to pursue a path 
which is a true ellipse, for the attraction of other bodies, in particular 
the sun, pulls her away from that path. So the moon's center sometimes 
recedes to a distance of 253,000 miles, and approaches as near as 
221,000 miles. 

What is Parallax ? — The moon's distance is found by 
measuring the parallax. Parallax is change in apparent 
direction of a body due to change of the point of observa- 
tion. It is by no means so puzzling as it may look. 




Parallax decreases as Distance increases 



Place a yardstick on its edge at the farther side of a table, as shown. 
Set up a pin, a nail, and a screw, at convenient intervals ; the nail at 
twice, and the screw at three times, the distance of the pin from the 
notch in the card between the eyes. It is better if notch, pin, nail, and 
screw are in a straight line nearly at right angles to the yardstick at its 
middle point. First, from the aperture in the card at a, observe and 
set down in a horizontal line the readings of pin, nail, and screw, as 
projected against the rule ; then repeat the observation from b^ in the 
same order, setting down readings in line underneath. Screw, nail, and 
pin all seem to change their direction as seen from the two apertures. 
This apparent change of direction is parallax ; it is the angle formed 
at the object by lines drawn from it to each eye. Now take the differ- 
ences of the pairs of readings as they stand: the difference of the pin 
readings is twice that of the nail readings, and three times that of the 



Moo7is Parallax at Differe^it Altitudes 235 

screw readings. Parallax, then, is less, the farther an object is removed 
from the base, or line joining the two observation points. And con- 
sidering these points fixed, we reach the general law that — 

Tlie parallax of an object decreases as its perpendicular 

dista7ice from the base of observation increases. 

The Moon's Equatorial Parallax. — In measuring celestial 
distances, obviously it is for the interest and convenience 



gz: 



Size and Distance of Earth and Moon in True Proportion 



of all astronomers to agree upon some standard by which 
to measure and indicate parallaxes. Such a standard line 
has been universally adopted ; it is the radius of the earth 
at the equator. The moon's parallax, then, is the angle at 
the center of that body subtended by the equatorial radius 
of the earth. This 
constant of lunar 
parallax is nearly a 
degree in amount 
(57' 2'^). It means 
that an astronomer, 
if he could take his 
telescope to the 
moon and there 
measure the earth, 
would find its equa- 
tor to fill twice the 
angle of the moon's 
equatorial parallax ; 
that is, the earth 

would be 1° 54^ in diameter — an angle correctly repre- 
sented in the slim figure near the top of the page. 

Moon's Parallax at Different Altitudes. — Whatever the 




Parallax increases with Zenith Distance 



236 The Mo 071 

latitude of the place, the moon's parallax is the angle 
filled by the radius of the earth at that place, as seen 
from the moon. When moon is in horizon, that radius 
AC (preceding diagram) is perpendicular to the horizon 
AB, and the parallax AMC is consequently a maximum, 
called the horizontal parallax. Higher up, as at M\ change 
in apparent direction of the moon, as seen from A and C, 
is less; that is, the parallax is less. With the moon at 
M^\ in the zenith, the parallax becomes zero, because 
the direction of M^^ is the same, whether viewed from A 
or C. Thus we derive the important generalization, true for 
sun and planets as well as moon : For a heavenly body at a 
given distance from the earth's center parallax increases 
with the ze7iith distance. 

Parallax lessens the Altitude. — True altitude of the 
moon and other bodies is measured upward from the ra- 
tional horizon to the center of the body. In the diagram 
on the previous page, these altitudes are HCM, HCM\ 
and HCM'\ But as seen from the point of observation 
A, the moon's apparent altitudes are 0° at B, BAM' , and 
BAM" . It is clear that these altitudes must always be less 
than the true altitudes, except when moon is in zenith. 
And by inspection we reach the general proposition that 
parallax lessens altitude, and its effect decreases as altitude 
increases, until it becomes zero when the body is exactly 
in the zenith. Both parallax and refraction vanish at 
the zenith ; but at all other altitudes, their effects are 
just opposite, refraction always seeming to elevate, and 
parallax to depress, the heavenly bodies. 

How the Distance of the Moon is found. — By precisely 
the principle of the illustration on page 234 is the distance 
of the moon from the earth found — that is, by calculation 
from its parallax. And the parallax can be found only by 
observations from two widely distant stations on the earth. 



Mooiis Deviation from a Straight Line 237 



Imagine a being of proportions so huge that his head would be as 
large as the earth. Then think of- his two eyes as two observatories ; 
for example, Berlin and Capetown, one in the northern and one in the 
southern hemisphere. Also imagine the moon to take the place of the 
screw and replace the divisions on the rule by fixed stars. Evidently 
then, the observer at Berlin will see the moon close alongside of differ- 
ent stars from those which the Capetown observer will see adjacent 
to the edge. The amount of displacement can be judged from this 
illustration, which shows the well- 
known group of stars called the 
Pleiades in the constellation Taurus. 
The bright disk represents the moon 
as seen from Berlin, the darker disk 
where seen from Capetown. As the 
angular distances of all these stars 
from each other are known, the an- 
gular displacement of the moon in 
the sky (or its parallax referred to 
the line joining Berlin and Capetown 
as a base) can be found. Xow the 
length of this straight line, or cord. 
through the earth's crust is known. 
because the size of the earth is 
known. So it is evident that the 
distance of the moon can be calcu- 
lated from these data. The process, 
however, requires the application of 
methods of plane trigonometry. It 
w^as primarily for the purpose of find- 
ing the moon's distance that the Royal Observatory at Capetown was 
founded by the British government early in the present century. 

Moon's Deviation from a Straight Line in One Second. — 

As the moon's distance from the earth is approximately 
240,000 miles, the circumference of her orbit (considered 
as a circle) is 1,509,000 miles. But our satellite passes 
over this distance in 27 d. 7 h. 43 m. 1 1.5 s. ; therefore in one 
second she travels 0.604 mile. In that short interval how 
far does her path bend away from a straight line, or tan- 
gent to her orbit } 

Suppose that in one second of time the moon would move from S 
to T^ if the earth exerted no attraction upon her. On account of this 




Moon as seen fron-i Berlin and 
Capetown -* 



238 



The Moon 



attraction, however, she passes over the arc .9/. This arc is 0.604 i^iile 
in length, or about o" .^ as seen from the earth; and as this angle is 

very small, the arc St may be re- 
garded as a straight line, so that StU 
is a right angle. Therefore 

SU \ St :\ St : Ss 

But SU is double the distance of the 
moon from us ; therefore Ss is 0.053 
inch, which is equal to 77, or the 
distance the moon falls from a straight 
line in one second. 



So that we reach this re- 
markable result : The curva- 
ture of the moon's path is so 
slight that in going -^-^ of a 
mile, she deviates from a 
straight line by only ^V ^^ ^^ 
inch. 
- First her apparent diameter is 




Fall of Moon in One Second 



Dimensions of the Moon. 

measured : it is somewhat more than a half degree (accu- 
rately, the semidiameter is 15^ 32^^6). But the moon's 
parallax, or what is the same thing, the angle filled by the 
earth's radius as seen from the moon, is 57^ So that, 
as the length of the earth's radius is 3960 miles, we can 
form the proportion — 



i Radius of earth ) 
\ as seen from moon \ 

57 



i Radius of moon ) 
\ as seen from earth \ 

15-5 



i Length of earth's ) 
' radius in miles 



3960 



Length of moon's ) 
radius in miles \ 

1077 



The diameter of the moon, therefore, from this proportion 
is 2154 miles. A more exact value, as found by astrono- 
mers from a calculation by trigonometry is 2160 miles. The 
moon's breadth, then, somewhat exceeds one fourth the 
diameter of our globe. So far as known, the diameter is 
the same in all directions ; that is, the moon is spherical. 
As surfaces of spheres vary with the squares of their 



To Measure the Moon s Diameter 



239 



diameters, the surface-area of our satellite is about -^^ that 
of our planet, or 4| times that of the United States. The 
bulk of the moon is only -^^ that of the earth, because 
volumes of globes vary as the cubes of their diameters. 

To measure the Moon^s Diameter. — You need not take the diameter 
of the moon on faith : measure it for yourself. When our satellite is 







Measuring the Moon's Dianaeter without Instrunaents 



within a day or two of the full, select a time from a half hour to three 
hours after moonrise. Open a window with an easterly exposure, close' 
one of the shutters, and turn its slats (opposite the open sash) so that 
their planes shall be directed toward the moon. The observation now 
consists of four parts : (i) so placing the head that the moon can be 
seen through the slats, (2) making the distance of the eye from the 
window such that the moon will just seem to fill the interval between 
two adjacent slats, (3) measuring the eye's distance from the slats, (4) 
measuring the distance of the slats from each other. A pile of books 
will be a help in fixing the point where the eye was when making the 
observation. Placing the head beyond the books, and about seven feet 
from the sash, move slowly away from the window till the moon just 
fills the space between two adjacent slats. Or if size of the room will 
allow, let the moon fill the space between two slats not adjacent. Make 
a mark on the frame of the shutter between these slats. Bring the pile 



240 The Moon 

of books close up to the eye so that a near corner of the top book may 
mark where the eye was. Next thing necessary is a non-elastic cord 
about 15 feet long. Tie one end to the slat or frame, near mark just 
made, then draw it taut to corner of pile of books where the eye was. 
Measure along the cord the distance (in inches) of the eye from the 
slats. Also measure perpendicular distance (in inches) between the 
inner faces of the tw^o slats marked. Then approximate diameter of 
moon (in miles) is found from the following proportion : — 

f Distance of 1 f distance of 1 f diameter of 

\ slats from \ : \ slats from 1^ : : 239,000 : { the moon 
I the eye J I each other J I (in miles) J 

Repeat observation at least twice, moving pile of books each time, 
adjusting it anew, and measuring distance over again. 

Measures of the Moon and their Calculation. — On i8th 
January, 1897, at about 6 o'clock p.m., or an hour after 
the moon had risen, the following measures were made: — 



Distances of 


Perpendicular distance betweei 


shutter from eye. 


inner faces of slats. 


(i) 139.5 inches. 


\\ inches. 


(2) 136 


239,000 


(3) 137 


59.750 


137.5 average. 


137.5)298750 




2170 



So the moon's diameter from these crude measures is 
2170 miles, only about 200" P^^^ ^^^ great. 

Why the Moon seems Larger near the Horizon. — Because of an 

optical illusion. With two strips of blank paper, cover everything 
near the bottom of this page except the line of dots. Before reading 
further, decide which seems longer, xy ox yz"^. 



Distance almost invariably seems longer if there are many interven- 
ing objects. For example, xy seems longer than j^-, because xy\^ 
filled with dots, and yz is not. Thus horizon appears to be more 
distant than zenith, because the eye, in looking toward the horizon, 
rests upon many objects by the way. This accounts for the apparent 
flattenino: of the celestial vault. Now the moon near the horizon and 



Moon really Largest at the Zenith 241 

at the zenith is seen to be the same object in both positions ; but when 
near the horizon she seems larger because the distance is apparently 
greater, the mind unconsciously reasoning that being so much farther 
awa\-. she must of course be larger in order to look the same. Often the 
sun is seen through thick haze or fog near the horizon, and a like 
illusion obtains. " But we know that the true dimensions of these bodies 
do not vary in this manner, nor do their distances change sufficiently. 
And whether illusion of sun or moon, it is easy to dispel. Roll a thin 
sheet of paper round a lead pencil, making a tube about 12 inches 
long. With one eye look through this tube at the much-enlarged sun 
or moon near the horizon ; instantly the disk will shrink to normal pro- 
portions. Then close this eye and open the other — as instantly the 




Why the Moon is really largest at the Zenith 

illusion deceives again. Repeat the experiment, opening and closing 
the eyes alternately as often as desired ; the eye behind the tube is 
never deceived, because it sees only a narrow ring of sky round the 
moon, and the tube cuts off all sight of the intervening landscape. 

Moon Larger at Zenith than at Horizon. — The actual fact is just the 
reverse of the illusion ; for if the moon's horizontal diameter is measured 
accurately when near the horizon, it is actually less than on the meri- 
dian. The above diagram makes this at once apparent. The moon 
at M is in the horizon of a place A on the surface of the earth, and 
in the zenith of B^ which may be conceived the same as A^ after the 
earth has turned about 90° on its axis. As M is nearer B than A by 
almost the length of the earth's radius, or nearly 4000 miles, clearly the 
zenith moon must be larger than the horizon moon by about -^^ part 
because CB is about ^^ of CM. 

The Moon's Mass. — The mass of the moon is 81 times 
less than that of the earth ; partly because of her smaller 
size, and partly because materials composing our satellite 
are on the average only three fifths as dense as those of 
the earth. 

todd's astron. — 16 



242 The Moon 

Gravity at the moon's surface is about \ that of the, earth : it is less 
by 8^- P^^'t because of the moon's smaller mass ; but greater by 14 
times because, as will be explained in a later chapter, gravity increases 
as the square of the distance from the center of attraction becomes less ; 
and the square of the moon's radius is about 14 times less than the 
square of the earth's. Surface gravity on the moon is therefore \\^ or 
about I, that on the earth. So a man weighing 144 pounds would 
weigh only 24 pounds on the moon, if weighed by a spring balance. 
An athlete who is applauded for his standing jump of 78 inches could, 
with no greater expenditure of muscular energy, jump 39 feet on the 
moon. Probably this deficiency of attraction at the moon's surface 
explains, too, why many of the lunar mountains are much higher than 
ours. Our satellite's attraction for the oceans of the earth, produc- 
ing tides, is a basis of one method of weighing the moon. Another 
method is by the moon's influence on the motion of the earth : Avhen 
in advance, or at third quarter the moon's attraction quickens our motion 
round the sun as much as possible ; when behind the earth in its orbit, 
or at first quarter, our satellite retards our orbital motion round the 
sun by the greatest possible amount. 

Axial Rotation. — Our globe revolves on its axis about 
30 times more swiftly than the moon does. For while 
our day is 23 h. 56 m. long, the lunar day is equal to 29I 
of our days; that is, the moon turns round once on her 
axis while going once round the sun. 

The simplest sort of an experiment will clearly illustrate this : let a 
lighted lamp represent the sun ; the teacher standing in the middle of 
the room represent the earth ; and let a pupil, representing the moon, 
walk slowly around the teacher in a circle, the pupil being careful to 
keep the face always turned toward the teacher. It will readily be seen 
that the pupil while walking once around has turned his face in succes- 
sion tow^ard all objects on the wall. In other words, he will have made 
one slow revolution on his own axis in exactly the same time it took 
him to walk once completely round the teacher. So the two motions 
being accomplished in just the same time, a given side of the moon is 
always turned toward the earth, just as the face of the pupil was always 
toward the teacher. So, too, the opposite side of our satellite is per- 
petually invisible to us. 

Librations. — By a fortunate dip of the moon's axis to 
the plane of the orbit, however, we are sometimes enabled 



No Licnar Atmosphere 243 

to see a little more of the region, now around one pole, and 
now around the other. The inclination is 83° 2i\ and our 
ability to see somewhat farther over, as it were, arises from 
this libration in latitude. Again, the rate of the moon's 
motion about the earth varies, while her axial turning is 
perfectly uniform, so that one can see around the edge 
farther, alternately on the western and eastern sides ; 
this is called libration in longitude. When the moon 
is near the zenith, there is little or no effect of libration 
due to position of observer on the earth. When, however, 
the moon is in the horizon, observer is nearly 4000 miles 
above the plane passing through earth's center and the 
moon. Consequently he can see a little farther around 
the western limb at moonrise and around the eastern limb 
at moonset. This effect is known as diurnal libration. 
As a sum total of the three librations, about four sevenths 
of the moon's entire surface can be seen in all. 

No Lunar Atmosphere. — One reason for our certainty 
that the moon has no atmosphere is this : when our sat- 
ellite passes over a star (or occults it, as the technical 
expression is), disappearance at the edge of the moon is 
exceedingly sudden. There is no dimming of the star's 
light before it is extinguished, as there would be if partly 
absorbed by lunar air and clouds. The spectroscope, too, 
shows no change in the star's spectrum when it is close to 
the moon's edge. Also during solar eclipses, the moon's 
outline seen against the sun is always very sharply defined. 
Some writers have thought it possible that there may be 
traces of water and atmosphere yet lingering at the bottom 
of deep valleys, but no observations have yet confirmed 
this hypothesis. Perhaps the moon, in some early stage 
of her history, had an atmosphere, though not a very ex- 
tensive one ; and it may have been partly absorbed by 
lunar rocks during the process of their cooling from an 



244 ^/^^ Moon 

original condition of intense heat, common to both earth 
and moon. Comstock is investigating anew the question 
of a kmar atmosphere. 

Why No Air and Water on the Moon. — Supposing that these ele- 
ments once surrounded the moon in remote past ages, their absence 
from our satellite at the present time is easy to explain according to the 
kinetic theory of gases, accepted by modern physicists. This theory 
asserts that the particles of a gas are continually darting about in all 
possible directions. The molecules of each gas have their own appro- 
priate or normal speed, and this -may be increased as much as seven 
fold in consequence of their collisions with one another. From the 
known law of attraction it is possible to calculate the velocity of a mov- 
ing body which the moon is capable of overcoming ; if a rifle ball on 
the moon w^ere fired with a velocity of about 7000 feet per second, or 
three times the speed so far attained by artificial means on the earth, 
it Avould leave our satellite forever, and pursue an independent path in 
space. Physicists have ascertained that the molecules of all gases 
composing the atmosphere can have velocities of their own far exceed- 
ing this limit ; and as earth and moon are many millions of years old, 
it is easy to see how the moon may have completely lost her atmos- 
phere by this slow process of dissipation. Surface attraction of the 
moon, only one sixth that of the earth, has simply been powerless to 
arrest this gradual loss. The possible speed of molecules of hydrogen 
is greatest, and even exceeds the velocity which the earth is able to 
overcome ; so that this theory explains, too, the absence of free hydro- 
gen in our own atmosphere. Water on the moon would gradually 
become vaporized into atmosphere, and complete disappearance as a 
liquid may readily have taken place in this manner. Whether it may 
be present in the form of ice, it is not possible to say. 

The Moon's Light and Heat. — The amount of moonlight 
increases from new to full more rapidly than the illumined 
area of the moon's disk; so our satellite at the quarter 
gives much less than half her light at the full. Mainly, 
this is due to gradually shortening shadows of lunar eleva- 
tions, which vanish at the full. As is very apparent to 
the eye at this phase, some parts of the moon are much 
darker than others ; but on the average, the lunar surface 
reflects about one sixth of the sunlight falling upon it. 
The spectroscope shows no difference in kind between 



The Moon and the Weather 245 

moonlight and sunlight. The brightness of the full moon 
is deceptively small, being at average distance only ^ ^ ^^^ ^ ^ 
that of the sun. Heat from the full moon is nearly four 
times greater than the amount of light, and the larger 
part of it is heat, not reflected, but radiated from the moon 
as if first absorbed from the sun. Our satellite having no 
atmosphere to help retain this heat, it radiates into space 
almost as 'soon as absorbed, so that temperature at the 
lunar surface, even under vertical sunlight, probably never 
rises to centigrade zero. At the end of the fortnight 
during which the sun's rays are withdrawn, temperature 
must drop to nearly that of interplanetary space, proba- 
bly about 300° below zero. In America Langley and 
Very are foremost in this research. 

The Moon and the Weather. — A wide, popular belief, hardly more 
than mere superstition, connects the varying position of the lunar 
cusps with the character of weather. The line of cusps is continu- 
ally changing its angle with the horizon, according to the relation of 
ecliptic (or moon's orbit) to the horizon, as already explained; and 
it is impossible, therefore, to see how or why this should indicate a 
wet moon or a dry moon. As for changes of weather occasioned by, 
or occurring coincidently with, the moon's changing phases, one need 
only remember that the weekly change of phase necessarily comes near 
the same time with a large per cent of weather changes ; and these 
coincidences are remembered, while a large number of failures to coin- 
cide are overlooked and forgotten. Weather, too, is very different at 
different localities, and probably there is always a marked change going 
on somewhere when our satellite is advancing from one phase to 
another. Critical investigation fails to reveal a decided preponderance 
either one way or the other, and any seeming influence of the moon 
upon weather is a natural result of pure chance. The full moon, too, is 
popularly believed to clear away clouds ; but statistical research does 
not disclose any systematic effect of this nature. Moon's apogee and 
perigee are known to occasion a periodic disturbance of magnetic 
needles, and may possibly be concerned in the phenomena of earth- 
quakes ; but the latter effect is not yet fully established. 

Surface of the Moon. — In days of earlier and less perfect 
telescopes, darker patches very noticeable on the moon's 



246 



The Moo7i 



disk were named seas, and these titles still cling to them, 
although it is now known that they are only desert plains, 
and not seas. All the more, important features can be 
accurately located from the accompanying illustration. 




Telescopic Features of the Moon as seen in an Inverting Telescope 



Since great modern telescopes, using a power of 1500 bring 
the moon within about 150 miles, much detail can be seen 
in the inexpressibly lonely scenery diversifying our satellite. 
A great city might be made out, but the greatest building 
ever built on our earth could not be seen except as a mere 
speck. Also the best modern photographs, like those re- 



Surface of tlie Moon 



247 



produced on pages 16 and 248, are amply sufficient for 
critical study ; and examination of them is much more 
satisfactory than the ordinary view through a telescope. 
The ' seas,' so-called, may in truth be the beds of primeval 



^o, 



^/?; 



^^ 



^>. 











Oo ^ 



^_^ o 

©Itycho O ^-^ 

/7T^^ SCHICKARD 

O Q ^^ Mare ^ 
O ^ ^O [^"railway' ^ Humorum 

CATHARINAr-N ARZACHElQ MaTG ©CASSENDi ^\o 

Mare Nectans ^ A /'^iiiPHONsus , \^ 

(JVENDELINUS r J ALBATEGNIUSl^ X^ O GRIMALDlfX \% 

rs THBOPH.US H,PPARCHUSr^S<"°""^ FLAMSTBEO p. \J A 5 

Wlangrenus V_y Qherschel U \Jj| 

Mare C) , (~\ ^ Oceanus \\ z 

,i.MASKELYNE TRIESNECKER Q ^ |h 

Fcscunditatis '>i^ Mare /^ Q ,^, ^^^^P""^" - 



^ 



:ASTOF 





fracastor 




Q^GEMI 



Mare r'^\:^ 

Tranquillitatis stadiusQ ^^^?c0PERNICUS Procellarum 

3 O ERATOSTHENES (q) q 

Q '^^^Ir HERODOTUS I 

Oq Mare ^^^^ aristarchusOO 

p, /^ ^-^archimedes 

^ 5e renitati s q U ^ 

Mare 

.,,,^ ARISTILLUSV' 



EUDOxus^ .ueXALPS 

ATLAS ^^HERCULES 



m b r i u m 



Op 



ARISTOTLE 



NORTH POLE 

Key to the Chart of the Moon Opposite 



oceans, which have dried up and disappeared hundreds of 
thousands of years ago. They are not all at the same 
level. Earlier stages of cosmic life are characterized by 
intense heat ; but as development of the moon progressed, 
original heat gradually radiated into space, leaving her 
surface finished. Evidently she has gone through experi- 



248 



The Moon 



ences some of which the earth may already have known, 
and through others still in our remote future. • Being so 

much smaller 
than the earth, 
as well as less in 
mass, our satel- 
lite cooled much 
faster than the 
parent planet. A 
few surface feat- 
ures are to be 
explained as due 
to the consequent 
shrinkage. 

Maps and Pho- 
tographs of the 
Moon. — All the 
lunar mountains, 
plains, and cra- 
ters are mapped 
and named; and 
astronomers are 
quite as familiar 
with ' Coperni- 
cus ' and ^Eratos- 
thenes ' (a great 
crater, and a 
mountain nearly 
16,000 feet high) 
as geographers 
are with Vesu- 
vius and the 
Matterhorn. Hevelius of Danzig made the first map of 
the moon in 1647. He named the mountains and craters 




Moon's North Cusp (photographed by the Brothers Henry 
of the Paris Observatory) 



TJic Mountains on the Moon 249 

and plains after terrestrial seas and towns and mountains. 
But Ric'cioli, who made a second lunar map some time 
after, renamed the moon's physical features, immortalizing 
in this way himself and many friends. His names, with 
numerous modern additions, are still current. 

One astronomer has counted 33,000 craters on the moon, of course on 
only the four sevenths of her surface ever turned toward as ; and as there is 
no reason for supposing the remainder to contain features differing in kind 
from those on the hemisphere so famiUarly known, probably there are 
not less than 60,000 craters on the entire surface of our satellite. Dur- 
ing the last half century many astronomers liave interested themseh^es 
in producing photographs of the moon, with very remarkable success. 
By an exposure of a second or two, a vast degree of detail is secured 
with perfect accuracy, w4iich the pencil could not depict in months ; in- 
deed, critical study with a microscope has brought to light lesser features 
of hill and valley which had escaped the eye and the telescope alone. 
Photographic maps or atlases of the moon on a very large scale have 
recently been published by the Paris Observatory, the Lick Observatory, 
and the Prague Observatory ; and the material already accumulated will, 
during the next century, show^ any considerable changes, should such be 
taking place. 

Changes on the Moon. — Probably the observers who a century ago 
recorded volcanoes in activity and progressive changes on the moon 
were deceived by the highly reflective character of materials forming 
the summits of certain mountains. Some craters are alleged to have 
disappeared, and in other instances new craters to have formed ; but 
evidence has in no case amounted to absolute proof as yet. It is still 
an open question whether surface activity of any kind characterizes the 
lunar disk, except perhaps on a very small scale, too minute for detection 
with present instrumental means. Varying conditions of illumination 
by the sun are so marked, even from hour to hour, that nearly all 
reputed changes are sufficiently explained thereby. Size and power 
of the telescope, and in drawings the personal equation of the artist, 
together with the state of atmosphere, all tend to introduce elements 
making sketches far from comparable. 

The Mountains on the Moon. — Although of all the satel- 
lites of the solar system, the moon is nearest the size and 
mass of its primary, still this neighbor world is no copy of 
the present earth. The difference between them is accentu- 
ated in the character of their mountains — on the earth 



250 



The Mooft 



ridges and mountain chains for the most part, with rela- 
tively few craters ; on the moon quite the reverse, craters 
being far in excess. In large part they seem to be volcanic 
in formation, but many of the largest ones with low walls 
are probably ruins of molten lakes. When the mountains 
of the moon are illuminated by a strong cross-light — as 
along the terminator at sunrise and sunset — they are 




f^'-!,^ 


- 1 


1 


^ 




BA Y 


Jul 


or 


NAPLES 


i 


f 




j 



Lunar Volcanoes 



Terrestrial Volcanoes 



thrown into sharp relief, as in this picture of lunar vol- 
canoes, set opposite a model of Vesuvius and neighboring 
volcanoes photographed under like circumstances of 
illumination. Similar volcanic origin is self-evident. 

Nearly 40 lunar peaks are higher than Mont Blanc, and the greater 
relative height of lunar than terrestrial peaks is doubtless due to lesser 
surface gravity of our satellite. The Leibnitz Mountains, perhaps the 
highest on the moon, are 30,000 to 36,000 feet in elevation, much 
exceeding the highest peaks on earth. As there is no softening atmos- 
pheric effect, shadows of all lunar objects are so sharply defined that 
the height, depth, and extent of nearly all natural features of the moon's 
surface can be accurately measured. 



The Lunar Cliff's 



251 



To find the Height of a Lunar Mountain. — Heights of many moun- 
tains on the moon have been found by this method : with a suitable 
instrument, called the 
micrometer, attached 
to the telescope for 
measuring small arcs, 
measure AM, distance 
of terminator from 
peak of a mountain 
which sunlight from 
S just grazes. Length 
of moon's radius AD 
is known, and distance 
AM is given by the 
measures. So the value 
oiBM, or moon's aver- 
age radius as increased by the height of mountain, can be found by 
solving the right-angled triangle ABM. 




Measuring Height of a Lunar Mountain 



A Typical Crater highly magnified. — Somewhat north 
and east of the center of the lunar disk is the great crater 
Copernicus. Rising from its floor is a cluster of conical 
mountains about 2500 feet high. The walls of the crater 
itself are about 50 miles in diameter, and 13,000 feet high. 
As the drawing on next page shows, the surroundings of 
Copernicus are rugged in the extreme, and near full moon a 
complex network of bright streaks may be seen extending 
more than a hundred miles on every side. They do not 
appear in the illustration because it was drawn near the 
quarter. The streaks do not radiate from the great crater 
itself, but from some of the craterlets alongside, by which 
Copernicus is especially thickly surrounded. Probably the 
streaks are due to light-colored gravel or powder scattered 
radially. Most of the adjacent craterlets are very minute, 
and they are counted by hundreds. 



The Lunar Cliffs or Rills and Other Features. — Almost at the center 
of the moon, but slightly toward the northwest, is Triesnecker. a well- 
pronounced crater, along the wxst side of which is the remarkable cliff 



252 



The Moon 



system shown opposite. Their radiation and intersection are strongly 
marked — chasms about a mile in breadth, and nearly .300 miles in 
length. Little is known about their nature and even less about their 
origin. The bottom of the cliiTs is seen to be nearly flat, presenting 
to some extent the appearance of an ancient river bed. The few moun- 
tain chains on the moon resemble those on the earth in one respect: 

they are much 
steeper on one side 
than on the other, 
as if the tiltings had 
been similarly pro- 
duced. Craggy and 
irregular pyramids 
are sparsely scat- 
tered on the plains. 
There are many 
valleys, some wide 
and deep, others 
mere clefts or 
cracks. The term 
;'/// is often applied 
to them although 
waterless, and there 
are many hundreds, 
passing for the most 
part through seas 
and plains, though 
occasionally inter- 
secting the craters. 
Some are straight, 
others bent and 
branching. Possi- 
bly they are fissures 
in a surface still 
shrinking. In a few 
instances, the geo- 
logical feature 
known as a fault may be observed — the crack is not an open one, 
and the surface on one side is higher than on the other. Also there 
are walled plains, from 40 to 150 miles in diameter, with interiors 
generally level, but broken by slight elevations and circular pits or 
depressions. Nearly the entire visible surface is astonishingly diver- 
sified by clean-cut irregularities looking much as if neither water nor 
atmosphere had ever been present on the moon. Even a small 




Region Surrounding Copernicus (highly magnified) 



If One Were to Visit the Moon 



253 



telescope helps greatly in examining them, and their position on or 
near the terminator is most favorable for their study. Intervals of a 
double lunation, or 59 d. i J h. bring the terminator through very nearly 
the same objects, so that the nature and extent of illumination are 
comparable. 

If One were to visit the Moon. — Of course no human being could 
visit the moon without taking air and water along with him. But what 
we know about the surface of our satellite enables us to describe some 
of the natural phenomena. 
Absence of atmosphere 
means no diffused light; 
nothing could be seen 
unless the direct rays of 
the sun were shining upon 
it. The instant one 
stepped into the shadow 
of a lunar crag, he would 
become invisible. No 
sound could be heard, 
however loud ; in fact, 
sound would be impossi- 
ble. A landshde, or the 
rolling of a rock down the 
wall of a lunar crater, could 
be known only by the 
tremor it produced — 
there would be no noise. 
So slight is gravity that a 
good player might bat a 
baseball half a mile with- 
out trying very hard. 
Looking up, the stars 
would be appreciably 
brighter than here, in a 

perpetually cloudless sky. Even the fainter ones would be visible in 
the daytime quite as well as at night. If one were to land anywhere on 
the opposite side of the moon and remain there, the earth could never be 
seen ; only by coming round to the side toward our planet would it become 
visible. Even then the earth would never rise or set at any given place, 
but it would constantly remain at about the same altitude above the 
lunar horizon. Earth would go through all phases that the moon 
does here, only they would be supplementary, full earth occurring 
there when it is new moon here. Our globe would seem to be about 
four times as big as the moon appears to us. Its white polar caps of 




Triesnecker and Lunar Rills 



254 



The Moon 



ice and snow, its dark oceans, and the vast but hazy cloud areas 

would be conspicuous, 
seen through our upper 
atmosphere. Faint stars, 
the filmy solar corona, also 
the zodiacal light, would 
probably be visible close 
up to the sun himself; but 
although his rays might 
shine for a fortnight with- 
out intermission upon the 
lunar landscape, still the 
rocks would probably be 
too cold to touch with 
safety. 

From the chief lu- 
minary of our nightly 
skies, we turn to an 
investigation of dis- 
coveries made by 
astronomers concern- 
ing the orb of day, 
describing at the 
same time instru- 
ments and processes 
of the ' new astron- 
omy ' with which many of these researches have been 
conducted. 




Typical Lunar Landscape (Ml Earth) 



CHAPTER XI 

THE SUN 

MAN in the ancient world worshiped the sun. Prim- 
itive peoples who inhabited Egypt, Asia Minor, 
and western Asia from four to eight thousand 
years ago have left on monuments evidence of their vene- 
ration of the 'Lord of Day.' Archaeologists have ascer- 
tained this by their researches into the world of the 
ancient Phoenicians, Assyrians, Hittites, and other nations 
now passed from earth. A favorite representation of 
the sun god among them was the 'winged globe,' or 
'winged solar disk,' types of which are well preserved 
on the lintels of an ancient Egyptian shrine of granite in 
the temple at Edfu. In the Holy Scriptures are repeated 
allusions to the protecting wings of the Deity, referring 
to this frequently recurring sculptured design ; and we 
know that if his life-giving rays were withheld from the 
earth, every form of human activity would speedily come 
to an end. 

The Sun dominates the Planetary System. — The sun 
is important and magnificent beyond all other objects in 
the universe, not only to us, inhabitants of the earth, 
but to dwellers on other planets, if such there be. All 
these bodies journey round him, obedient to the power 
of his attraction. Upon his radiant energies, lavishly 
scattered throughout space as light and heat, is dependent, 
either directly or indirectly, the existence of nearly every 
form of life activity ; and the transformation of solar 

255 



256 



The Sun 



energy produces almost every variety of motion upon 
the earth, whether animate or inanimate. • The more 
primitive the civiHzation, the more apparent is the depend- 
ence of man upon the sun. 

Activities in Labrador here pictured are an excellent illustration. 
Without the sun's vitaHzing action, the trees, whose trunks and 
branches furnished the load on the sled, not to say the sled itself, 




In Labrador (.Activities originating in the Sun) 



could not have grown. The food, whether animal or vegetable, upon 
which the life and energy of man and dog depend, would not have 
been possible without the sun. Creatures of land and sea, whose 
skins provided the straps by which the sled is drawn, could not long 
live without warmth and vitality lavished by the sun. Nor must we 
overlook the farther fact pertaining to natural movements and phenom- 
ena of the air : for the sun provides even the breeze to bulge the sail, 
and he has raised from the sea and diffused over the land the mois- 
ture which descends as snow, for the sled to slide upon. In the 
complicated life of our hio^her civilization, the sun is still all-powerful, 
though the Hnks in the chain of connection are in places concealed. 
Our comforts and activities are largely dependent upon heat given out 
by burning coal ; but it was through the action of the sun's rays that 



Suiis Distance a Celestial Unit 



257 



forests in an early geologic age could wrest carbon from the atmosphere 
and store it in this permanent mineral form, so useful — one might 
almost say necessary — in the processes of modern life. In everything 
material the sun is our constant and bountiful benefactor. 



Sun's Distance the Unit of Celestial Measurement. — The 

distance between centers of sun and earth is the measur- 
ing unit of the universe. Although motions and relative 
distances of heavenly bodies may be known, still their 
true or absolute distances cannot be found with accuracy, 
unless the fundamental unit is itself precisely determined. 
It is as if one were to try to measure the size of a house 
with a lead pencil ; it would be possible to find the dimen- 
sions of the house in terms of the lead pencil, but the 
actual size of the building would not be known until the 
length of the pencil, or unit of measure, had been ascer- 
tained. The distance of the sun is this unit. A method 
of finding the distance of the moon has been given, but 
the sun's distance is too great to be measured in this way 
— even the whole diameter of the earth is not long enough 
to form a suitable base for the slender triangle drawn from 
its antipodes to the sun. 



For the proper application of this method of finding distances, the 
triangle included between distant object and the two ends of the base 
line, must be well-conditioned. Such a triangle is 
shown in the figure, in which the width of an 
impassable stream is found by measuring on the 
left bank a distance nearly equal to the breadth 
of the stream itself. An ill-conditioned triangle 
is one whose base is very short in comparison 
with its other two sides. Such a triangle is shown 
on page 235, where the base (or earth's diameter) 
is only 3V ^f ^^ other sides. Base remaining the 
same, the farther away the object, the more ill-con- 
ditioned the triangle. As the sun is nearly 400 
times farther than the moon, the relation of base 
to other sides is only y^^oo- The triangle is, therefore, so ill-condi- 
todd's astron. — 17 




Well-conditioned 
Triangle 



258 The Sun 

tioned that this direct method of finding the sun's distance becomes 
inapplicable^ and other methods are always relied upon. 

Finding the Sun's Parallax. — On those rare occasions 
when Venus, a planet nearer the sun than our earth is, 
comes in her path exactly between us and the sun, she 
moves like a small black dot across the shining disk. 
This happens but twice in each century. Two observers 
widely separate on our globe, will see Venus projected 
upon different portions of the sun's disk at the same time; 
as on page 234, pin is seen against different parts of scale 
when viewed through the two peepholes. So the apparent 
path of Venus across the sun will be farther south on the 
disk, as seen from northern station; and farther north as 
seen from southern one. Difference of the two paths leads 
by suitable calculation to a knowledge of the angle which 
radius of the earth fills, as seen from the sun. This angle 
is called the sun's parallax. Its value at the average dis- 
tance of the sun is called the mean parallax. The equa- 
torial radius of our planet is taken as the standard, the 
same as in the case of the moon ; also when the sun is on 
the horizon its parallax is a maximum, called the horizontal 
parallax. The accepted value of the sun's mean equatorial 
horizontal parallax is 8' ^8. This means that the sun is so 
remote that if one could visit him and look in the direction 
of the earth, our globe would appear to be only \f^ .6 
broad, an angle so small as to be invisible to the naked 
eye. A telescope magnifying at least four or five diam- 
eters would be necessary to see it. 

The Sun's Distance. — The sun's parallax and the length 
of earth's radius are data for a calculation by trigonom- 
etry, giving the distance of the sun equal to 93,000,000 
miles. Also this important element may be found by 
aberratio7i. Knowing the velocity of light, it is easy to 
calculate the speed which the earth must have in order to 



The Size of the Sitn 



259 



produce the known amount of aberration of the stars, 
called the constant of aberration. So it is found that the 
earth's actual velocity is something over \%\ miles in a 
second. From this the length of the circumference of the 
orbit traversed by the earth in 365^ days or one year is 
readily found, and from that the diameter of the orbit, the 
half of which is the mean distance of the sun. There are 
many other and more complicated methods of obtaining 
the distance of the sun, and they all agree within a small 
percentage of error. Subtracting o".oi from the parallax 
is equivalent to increasing the sun's distance about 105,000 
miles, and vice versa. 




As Distance from Shade is to Size of Image, so is Sun's Distance to his Diameter 



To measure the Size of the Sun. — Knowing the distance of the sun. 
it is very easy to observe and calculate his real dimensions. The method 
is similar to that by which the size of the moon was measured ; and dif- 
ferent only because of the superior intensity of the sun's light. Instead 



26o The Sun 

of looking directly at the sun, simply look at the image produced by the 
sun's rays through a tiny aperture. Every one has noticed sunlight 
filtering into a darkened room through chinks between the slats and 
frame of a blind or shutter. Oftentimes a series of oval disks may 
be seen on the floor. Their breadth depends upon {a) the diameter 
of the sun, and {b) their distance from the shutter. Each oval disk 
is a distorted solar image. If a sheet of paper is held at right angles 
to the direction of the sun, the oval disk becomes circular, and its 
diameter can be measured. But as the paper is carried toward the 
shutter, notice that the disk grows smaller and smaller. So you must 
measure its distance from the shutter also. Select a time when the 
sun is not exactly facing a window, but is a little to the right or left of 
it, though not more than an hour in either direction. On closing the 
shutters, and turning the slats, the chain of disks on the floor will usu- 
ally become visible. Examine them carefully when projected on a small 
white card, and select the one which has the sharpest outhne. Or, the 
blinds may be thrown open, and sunlight admitted through a pin-hole 
in the shade, as in last illustration. Attach a sheet of white paper to 
the cover of a book ; so support it that the surface of the paper shall 
be at right angles to the line from book to sun. With a sharply-pointed 
pencil, mark two short parallel lines on the paper, a little farther apart 
than the diameter of the bright disk. Move the paper back until the 
sun's image just fills the space between the two lines. Measure dis- 
tance between lines ; also with a non-elastic cord, measure distance 
from shade to paper on the book. This completes the observation. 

Calculating the Observation. — As in calculating the size of the moon 
when its distance is known, so in computing the dimensions of the 
sun, only the ^rule of three' is necessary. On 22d May, 1897, size of 
a pin-hole image of sun was measured and found to be 1.175 in. in 
diameter. Distance between the card on which the image fell and 
the aperture in shade was 10 ft. 5.4 in. So the proportion is — 

125.4 : 1. 175 :: 93,000,000 : x. 

The value oi x comes out 871,000 miles, or about j|o part too great. 
But this amount of error is to be expected, because the method is a 
crude one. Notice, however, its exactness in prihciple. To convey 
an adequate idea of the sun's tremendous proportions is practically 

impossible. 

How Astronomers measure the Sun. — The principle of 
their method is exactly the same as that just illustrated; 
and their results are more accurate only because their 
instruments are more delicate, and training in the use 





The Sun is a Sphere 261 

of them thorough and complete. The latest and best 
value of the sun's diameter is 865,350 miles. 

The best method utilizes an instrument called the heliometer, or sun 
measurer. It is a telescope of medium size, mounted equatorially ; but 
the essential point of difference is in the object glass, AB^ which is 
divided exactly in the middle. Accurate mechanical devices are pro- 
vided by which B can be slipped 
sidewise relatively to A^ as in 
the lower figure, and the precise 
amount of the motion recorded. 
Before the halves of the glass 
are moved apart, the sun's image 
is a single, very bright disk, like 
the left hand of the three Divided Object images of Sun in Heliometer 
here shown. Turn the screw SeTer°^ "'^'°" 
separating the halves of the 

glass, and overlapping images appear, as in the middle figure ; and by 
turning it far enough, the two images of the sun may be brought into 
exact exterior contact, as in the right hand of the three images. 
Final calculation of the sun's diameter is a tedious and complicated 
process, because a great variety of conditions and corrections must be 
taken into account ; but the heliometer is the most accurate measur- 
ing instrument employed by modern astronomers. The limit of 
accuracy of measurement with the heliometer is an angle no larger 
than that which a baseball would fill at New York as seen from 
Chicago. 

The Sun is a Sphere. — As the sun turns round on his 
axis, equatorial diameters are measured in every direction. 
As they do not differ appreciably from the polar diameter, 
the figure of the sun is a sphere. His real diameter is not 
subject to change; but as already shown, the sun's ap- 
parent diameter varies from day to day, in exact proportion 
to our change of distance from him. The mean value is 
almost 32' o'^ (according to Auwers, 31^ 59'^26). 

The actual diameter of the sun is difficult to determine, for a variety 
of reasons. The heat of his rays disturbs the atmosphere through 
which they travel, so that his outline, or limb, is rarely seen free from a 
quivering or wave-like motion. Another reason is irradiation, a physio- 
logical effect by which bright objects always seem larger than they really 



262 The Sm7z 

are. Irradiation increases as brightness of the object exceeds that of 
the background against which it is seen. Error in our knowledge of the 
sun's diameter is probably about j^oo P^-i't of the whole, or about 2''. 
At the distance 93,000,000 miles, i'^ of arc is equivalent to 450 miles, 
so that the amount of uncertainty in the diameter of the sun is about 
900 miles. 

The Sun's Volume, Mass, and Density, — As the sun's 
diameter is nearly no times greater than that of the 
earth, his volume is almost 1,300,000 times greater, be- 
cause volumes of spheres vary as cubes of their diameters. 
A method of measuring the mass of the sun is given on 
page 386. To put it simply, the sun's mass is found by " 
measuring the force of his attraction. If sun and earth 
are at the same distance from a given body, the sun will 
attract it 330,000 times more powerfully than the earth 
does. Sun's weight, in other words, is 330,000 times as 
great as earth's. A body falling freely under the influ- 
ence of the sun's attraction would on reaching him have a 
velocity of 383 miles a second. As the sun is 1,300,000 
times greater in volume than the earth, evidently he must 
be much less dense than our globe ; and his component 
materials, bulk for bulk, must be about one fourth lighter 
than those of the earth. As compared with water, the sun 
is rather less than i|- times as dense. 

Gravity at the Sun's Surface. — The weight of the 
earth, it will be remembered, is 6 x 10^^ tons. But the 
sun weighs 330,000 times as much, — a numerical result 
which the human mind is utterly powerless to grasp. 
Another comparison will help to fix relative proportions 
in memory. Many planets are vastly larger and more mas- 
sive than the earth. But if all the planets of the solar 
system and their accompanying retinues of satellites were 
fused together into a single ball, it would weigh but y\-^ ^s 
much as the sun. So vast are the dimensions of our cen- 
tral luminary that the force of gravity at the surface is not 



How to Observe the Stcn 



263 



so great as his prodigious mass would seem to indicate : 
it is only 27|- times as great as gravity at the surface 
of the earth. A 
body would fall ver- 
tically 444 feet in 
the first second. 
Recall the agile 
athlete who, when 
transferred to the 
moon, executed a 
standing jump of 
39 feet : if at the 
sun, he would find 
his movements 
hampered by a 
bodily weight of 
about two tons, and 
his ' standing jump,' 
if possible at all, 
could not exceed 

three inches. On the sun, the pendulum of an ordinary 
mantel clock would quiver or oscillate so rapidly that its 
vibrations could not easily be counted. For every tick of 
the escapement here, there would be five at the sun. 

How to observe the Sun. — Unless the telescope is provided with a 
special eyepiece, called a helioscope, it is dangerous to look at the sun 
directly, because heat rays coming through the dense colored glass cover- 
ing the eyepiece are very harmful to the delicate rods of the retina. 
Besides this, the colored glass is liable to be broken suddenly by the 
intense heat. If such accident happens while the, eye is at the tele- 
scope, a dark spot in the retina is pretty sure to result ; and it will re- 
main permanently insensitive — an extreme case of ^over-exposure.' 
Rather look at the sun's surface indirectly, by projection, as in the pic- 
ture. To the telescope tube attach a cardboard screen, two or three feet 
square, and fill the chinks around the tube with cloth or paper. This 
large screen tightly fastened to the tube, is very necessary to keep 




Viewing the Surface of the Sun 



264 



The Sun 



direct light of the sun from falling upon the sheet of paper below, on 
which the sun's image is projected. This sheet may be held in the 
hand ; but it is better to attach it to a light frame, which slides along a 
stick firmly screwed to the side of the telescope tube. Then the paper 

may be kept always at 
right angles to the axis 
of the telescope ; and 
spots may be made to 
look larger or smaller by 
merely sliding the frame 
toward or from the eye- 
piece. Careful focusing 
is important, and probably 
it will be necessary to re- 
focus every time the dis- 
tance between paper and 
eyepiece is changed. 
Ten or twelve persons 
can readily observe sun 
spots in this way at the 
same time, and without 
the slightest danger or 
inconvenience. Surface 
mottlings and faculae, or 
white spots, are finely 
seen. If the telescope is 
a large one, the eyepiece 
should occasionally be 
taken out and cooled ; 
but even a spyglass will 
gather enough light to 
show the spots and other 
details of the sun''s surface. 
The Photosphere. — The photosphere is that mottled exterior of the sun 
which radiates its light. The photographic picture above shows its general 
texture. The blurring is a real phenomenon. This rice-grain structure can 
nearly always be seen even with moderate telescopic power, because the 
grains are about 500 miles across. Under the best conditions of vision, 
and great increase of power, the grains subdivide into granules. Float- 
ing above the photosphere, and quite numerous around the sun's limb, 
may usually be seen a number of irregularly connected whitish spots, or 
patches, called faculae. It is certain that some of the faculae are eleva- 
tions, because they have been seen projecting beyond the edge of the 
disk. As will be shown farther on, the faculae extend in zones all the 




Photosphere (photographed by Janssen) 



Veiled Spots 



265 



way across the sun ; but they are more obvious at the limb, because 
general illumination of the photosphere in that region is less, owing to 
greater thickness of solar atmosphere through which rays from the 
photosphere must pass. 

Sun Spots. — Immense dark spots are frequently seen on 
the photosphere. Generally they have a dark center, 
called the umbra, and a somewhat lighter fringe, called the 
penumbra, which is 
darker near its outer 
edge, lighter toward 
the umbra, and often 
shows a thatch-work 
structure, as in Sec- 
chi's drawing (also 
page 11). Of widely 
varying shapes and 
sizes, they are usually 
nearly circular at the 
middle stage of exist- 
ence, though more 
irregular at beginning 
and end. 




Sun Spot highly magnified (Secchij 



The dark umbra is not all equally dark ; at times faint patches or 
grains of luminous matter appear to float above the darker region under- 
neath. Also sometimes appear tiny round spots, darker than the um- 
bra, known as nuclei — perhaps openings into still greater depths; for 
the spots themselves nearly always appear like depressions in the pho- 
tosphere, and on several occasions have been seen as actual notches 
at the edge of the sun, as in the next illustration. There is good 
evidence, however, that many of them are not depressions. If a spot 
is as large as 27,000 miles in diameter, it can be seen without a tele- 
scope as a very minute black speck. Occasionally spots are even larger 
than this, and 50,000 miles is a size not unknown. The largest sun spot 
on record was observed in 1858 ; it was nearly 150,000 miles in breadth 
and covered about ^^ of the whole surface of the sun. 

Veiled Spots. — Veiled spot is the name given to hazy, darkish 
patches appearing now and then upon all parts of the solar disk, even 



266 The Sun 

close to the poles. They have been seen to change their ill-defined 
outlines very rapidly. Not extensively observed as yet, they are never- 
theless regarded as kin to ordinary spots, only that the forces producing 
them are not intense enough to disrupt the photosphere. Faculae are 
often seen above them. 




EDGE OF ■ THE SUN i 



Many Spots are seen as Depressions at the Sun's Limb 

Formation and End of Spots. — Each spot or group of 
spots has its independent method of formation. Perhaps 
very gradual, through many weeks, spots have yet been 
known to attain full proportions in a few hours. When 
completed, they are roughly circular ; but as their end 
draws near, the surrounding matter seems to approach and 
crowd upon the umbra, as if to tumble pell-mell into its 
cavernous depths. Very likely this is what actually hap- 
pens. Often tongue-like encroachments of the penumbra 
force themselves across the umbra (illustrated in process 
on page ii); and this usually indicates the beginning of a 
rapid decline and disappearance. The chasm seems to be 
filled ; and only a slightly disturbed surface (surrounded by 
faculae or white spots, which soon disperse) remains for a 
brief time to indicate very indefinitely the place where 
the spot existed. Sun spots are easiest of all solar phe- 
nomena to observe. Sometimes exceptional disturbance 
sets up a motion so rapid and violent that vast changes 
have been seen within a few minutes' time, even while 
the observer was watching. 

Duration and Distribution of Spots. — Often spots are 
carried across the face of the sun in its rotation, and they 
become elliptical by foreshortening as they approach the 



Duration and Distribution of Spots 267 



edge and disappear. The following illustration shows how 
this takes place. If a spot lasts a fortnight or more, it will 
again come into view when the sun's rotation shall have 
carried it halfway round. On reappearing at the eastern 
limb, a spot is elliptical and very narrow at first, and grad- 




The Same Spot near Sun's Center and Edge 

ually it seems to broaden into its actual shape on facing 
the earth more and more squarely. The spots are, on an 
average, two or three months in duration, though very 
often lasting only a week, or perhaps even a few days or 
hours. The longest on record lasted 18 months, in the 
years 1840 and 1841. Spots do not appear on every part 
of the sun's disk, but they are nearly always confined to 
zones on both sides of the solar equator, extending from 
latitude 5° to 30°. The spots are most numerous in solar 
latitude 15°, both north and south, and a few more are seen 
in the northern than the southern hemisphere. 




6TH DECEMBER 5TH MARCH 5THjUNE 

Apparent Motion of Spots across the Sun 



5TH SEPTEMBER 



The sun's equator is tilted about 7° to the ecliptic, so that the spot 
zones appear sometimes straight and sometimes curved on the sun's 
disk, as the four figures show, for different seasons of the year. 



268 



The Sun 



Early in March the sun^s south pole, and early in September his north 
pole, is turned farthest toward us. The axis of the sun, if prolonged 
northward, would cut the celestial sphere near Delta Draconis. In 
April the sun's axis is inclined about 25° west of the hour circle passing 
through his center ; in October, about the same amount to the east of it. 



1.0 



Periodicity of the Sun Spots. — Spots are not always 
equally numerous on the surface of the sun. At times 
they may be counted by hundreds, and again days, and 
even weeks, will elapse without a single spot being visible. 
A well-estabhshed period is now recognized. Spots dimin- 
ish in number slowly, all the while appearing at lower and 
lower latitudes on the sun, and they pass through a mini- 
mum at about latitude 5° both north and south. Then 
rather suddenly there is an outbreak of spots, in latitude 

about 30^ on both 
sides of the sun's 
equator, followed by 
a growth in number 
and size of the spots 
to a maximum, after 
which again comes 

Curve of Sun Spots and Magnetic Declination ^j^^ decline in numbcr 

size, and latitude. As a new outbreak in high latitudes 
usually begins about two years before final disappearance 
of the zones of low latitude, it follows that near minimum 
the spots, although few in number, are distributed in four 
narrow belts, two of low and two of high latitude. The 
complete round, or spot period, is eleven years and one 
month in duration. From minimum to maximum is usually 
about five years, and from maximum to minimum about six 
years. The fluctuation in latitude is called Spoerer's Maw 
of zones.' Regarding as determinant of the true period, 
not merely the total number of spots, but the number 
as affected by the law of zones, the true sun-spot cycle 















/ 


-,J\ 


S^ 














/ 


V 




\ 


\ 










4 


/ 








% 


"^ 


~:r7Z^ 


^^ 


^-'■^ 


# 












i % 


i I 


\ 


•5 c 


1 \ 


2 s 




I I 


% % 


« 

3 S 



Famlce 



269 



appears to be about fourteen years long, because a new 
zone breaks out in high latitudes while the old one still 
exists near the equator. Neither the cause underlying the 
law of zones, nor the reason for the spot period itself, is 
known. Probably the latter is due to • the outbreak of 
exceptional eruptive forces held in check during the sea- 
sons of few^est spots. The last maximum occurred in 
1893, and the next minimum falls in 1899 or 1900. 

Do the Spots affect the Earth? — When sun spots are most numerous, 
displays of the aurora borealis are most frequent and brilliant, and the 
effects of magnetic storms are most strongly exhibited by fluctuations 
of magnetic needles delicately mounted in observatories, with pains- 
taking arrangements for recording all their oscillations. These effects, 
although recognized, are unexplained. Wolfer's diagram opposite shows 
how closely spot activity kept time with fluctuations of magnetic 
declination during the years 1886-96. Even in periods of largest and 
most numerous spots, the amount of heat received from the sun is not 
a thousandth part lessened, and any iefFect of periodicity of the spots 
upon the weather is too slight to be detected. 

Faculae. — On the bright surface of the sun may nearly 
always be seen still brighter specks or streaks, many 
thousand miles in length, 
and much larger than 
any of our continents. 
Such faculae were dis- 
covered by Hevelius, at 
Danzig, about the mid- 
dle of the 17th century. 
They are supposed' to 
be elevated regions of 
the surface, crests of 
luminous matter protrud- 
ing through the general 
and denser level of the 
photosphere. The fac- 
ulae are very numerous around the spots. The sun's atmos- 




Zones of Invisible Faculae, 7th August, 1893 
(photographed by Hale) 



270 The Suit 

phere absorbs a large percentage of its own light, so that 
the illumination of the disk diminishes gradually toward 
the edge all around. On this account the faculae are better 
seen near the edge ; but they exist in belts all the way 
across the sun's disk, and can be so photographed at any 
time by the spectroheliograph (described in a later sec- 
tion), although they are invisible to ordinary vision. These 
invisible facukTe are most abundant in the sun-spot zones. 
There is evidence that some faculae are clouds of incandes- 
cent calcium, an element strongly marked in the sun. The 
invisible faculae appear to be related to the prominences 
projected against the photosphere. 

The Sun's Rotation on his Axis. ^ The spots which last 
longest help most in ascertaining the time required by 
the sun in turning round once on his axis. A large num- 
ber of observations have shown that a long-lived spot near 
the sun's equator, starting from the center, will pass from 
east to west all the way round and return to the center in 
2 7^ days. But as the earth will meanwhile have moved 
eastward also, the sun's period of rotation, as referred to 
the stars, is 25^ days. This is the length of the true, or 
sidereal period. The exterior of the sun is not rigid, as 
the earth appears to be ; and it is found that spots remote 
from the equator give a longer period of rotation the 
higher their latitude. At latitude 45°, the period of the 
sun's rotation is about two days longer than on the equator. 
At latitude 75°, the rotation period, as found by Duner with 
the spectroscope, is 38^- days. Also Young, Crew, and 
others have verified the rotation in this manner in the 
equatorial regions. The cause of acceleration at the 
equator has not yet been discovered. 

The faculae appear to have a different law of rotation from that 
governing the spots ; for no matter what their latitude, they go round 
in less time than spots. From careful measures of numerous lines in 



Continuous Spectrum 271 

the solar spectrum, Jewell has found that acceleration of the sun's 
equator is greatest for the higher or outer parts of the solar atmosphere, 
and that the difference between the rotation periods of the sun's outer 
and inner atmosphere amounts to several days. 

The Spectroscope. — Place a prism in the path of a slender beam of 
sunlight. It will be refracted out of a straight course, and will emerge 
as a colored band. The light is all refracted, but it is not refracted 
equally ; the red is bent least, and the violet most. The many-colored 
image produced in this manner is called a spectrum. This unequal 
refraction, and decomposition of white light into its primary colors is 
called dispersion. Upon it depend the principles of spectrum analy- 
sis, which is a study of the nature and composition of luminous bodies 
by means of the light which they emit. Usually the spectroscope con- 
sists of four parts: (i) a very narrow slit S through which the beam 




A Single-prism Spectroscope in Outline 

of light is admitted, (2) a collimator, A^ or small telescope at whose 
focus the slit is placed, (3) a prism, P^ or a closely ruled surface, which 
effects the dispersion necessary to produce a spectrum, (4) a view 
telescope, BE^ for studying optically the different regions of the spec- 
trum. In researches of the present day, in which photography plays 
an important part, the spectroscope is usually constructed so that the 
eyepiece can be removed, and a plate-holder substituted in its place. 
Spectra can then be photographed, and afterward examined at leisure. 
The illustration on the next page shows a modern spectroscope as 
adapted for photographic work. Rays enter the upper tube on the left. 
Continuous Spectrum and Fraunhofer Lines. — Place a candle before 
the slit, and a continuous spectrum is produced. A continuous spec- 
trum is one w^hich is crossed by neither bright nor dark Hues ; the 
colors from red to violet blend insensibly from one to the other in 
succession. Replace the candle by a beam of sunlight, and observe 



272 



The Sun 



the difference : at first sight the spectrum appears to be continuous, 
but closer observation immediately shows that the band of color is 
crossed at right angles by a multitude of fine dark lines, of different 
widths and intensities, and seemingly without order of arrangement. 

This spectrum is a discontinuous spectrum. The dark 
lines are called Fraunhofer lines, from Fraunhofer, who 




Brashear's Universal, Spectroscope ^arranged for Photographic Research) 



first made a chart of their position -la the prismatic spec- 
trum. He designated the more strongly marked lines by 
the first letters of the alphabet, the A line being in the 
red, and the H line in the violet. Their character and 
position in the spectrum are highly significant ; for they 
indicate the chemical elements of which luminous bodies, 
especially the sun, are composed. 



Normal Solar Spectrum 



273 



Normal Solar Spectrum. — If the spectrum is formed by 
passing the rays through a prism, as in the illustration, 
(page 271), relative position of the dark lines will vary with 
the substance composing the prism P ; the amount of dis- 
persion in different parts of the spectrum varies with the 
material of the prism. Another method of producing the 
spectrum is therefore employed : by reflecting the sun's 
rays from a grating. A, accurately ruled with a diamond 




A Diffraction Spectroscope in Outline 

point upon poHshed speculum metal, thousands of lines to 
the inch, a diffraction spectrum is formed. In this case 
dispersion is entirely independent of the material of the 
grating ; and the spectrum is called the normal solar spec- 
trum, because the amount of dispersion of the rays is 
proportional to their wave length. 



<^E 




B k 



NORMAL 
SPECTRUM 



PRISMATIC 
SPECTRUM 



VLOLET GREEN RED 

Normal and Prismatic Spectra of Equal Length (Middle of both Spectra at D) 

The diagram gives a comparison of the two types of spectrum. The 
middle of the spectrum is practically coincident with the yellow D lines 
of sodium. As referred to the normal spectrum, the red end of a pris- 



todd's astron. ■ 



-18 



2 74 



The Su7i 



matic spectrum is very much compressed ; and its violet end similarly 
expanded. The finest gratings are ruled with a dividing engine perfected 
by Rowland. The precision of its working is such that the number of 
parallel lines which can be ruled on a plate of metal an inch square 
exceeds 20,000 ; but one tenth this number is a good working limit. 

High Power Spectroscopes. — The length of the spectrum 

varies with the degree of dispersion. It is evident that 
the greater the dispersion, the more the dark hnes will be 
spread out lengthwise in the spectrum, and separated from 
each other. It is as if magnifying power were increased. 
Consequently the higher the dispersion, the greater the 
number of dark lines which can be seen and photographed. 



When a greater degree of dispersion is required than one prism will 
produce, it is usual to employ an arrangement of many prisms, as shown 

in the figure. Light comes 
from the object glass of the 
collimator on the left, and 
passes round through several 
prisms successively, disper- 
sion becoming greater and 
greater, as indicated by the 
gradually widening white 
band, which finally passes 
into the observing telescope 
on the right. When prisms 
and their accompanying 
small telescopes are rigidly 
secured to the great tube in 
place of the eyepiece ordi- 
narily used with it, such a 
combination of the two in- 
struments is often called a 
telespectroscope. In the 

diffraction spectroscope, in- 

A High Power Prism Spectroscope r • u^- \^r.A 

^ F F crease of powder is obtained 

by passing to the spectrum of a higher order, which is obtained by 

tilting the grating at an angle suitable to the order (second, third, or 

fourth) of spectrum desired. In all cases, the higher the degree of 

dispersion, the fainter becomes the spectrum in every part. So that 

a practical limit is soon reached. 




Photographmg the Suns Spectrum 275 




Slit and the Comparison Pi ism 



Principles of Spectrum Analysis. — In 1858 Kirchhoff 
reduced to the following compact and comprehensive form 
the three principles underlying the theory of spectrum 
analysis: (i) Solid and liquid bodies, also gases under 
high pressure, give, when incandescent, a continuous spec- 
trum. (2) Gases under low 
pressure give a discontinuous 
spectrum, crossed by bright 
lines whose number and posi- 
tion in the spectrum differ 
according to the substances 
vaporized. (3) When white 
light passes through a gas, 

this medium absorbs rays of identical wave length with 
those composing its own bright-line spectrum. Therefore 
dark lines or bands exactly replace the characteristic bright 
lines in the spectrum of the gas itself. This principle, 
theoretically correct, is easily illustrated and verified ex- 
perimentally. These three fundamental principles fully 
account for the discontinuous spectrum of the sun, and 
the multitude of dark Fraunhofer lines which cross it. 

Photographing the Sun's Spectrum. — The principles of spectrum 

analysis just enunciated indicate clearly how to ascertain the elements 

composing the sun. The process is one of map- 

A. ping or photographing the lines in the solar spec- 

; : trum, and alongside of it in succession the spectra 

of terrestrial elements whose existence in the sun 

is suspected. This is effected by means of the 

comparison prism, ab^ shown above. It covers part 

of the slit, ;;/. Sun^s rays come from B^ pass into 

the comparison prism, are totally reflected, and pass 

through the slit (downward in the adjacent figure). 

Thus they appear to come from A^ the same as rays 

from the vaporized substance under examination ; 

and as both sets of rays then make the optical circuit 

of the spectroscope side by side, the field of view embraces solar 

spectrum and spectrum of the terrestrial substance, also side by 




Course of Rays in 
Comparison Prism 



276 



The Smt 



side. Direct comparison line for line is thereby greatly facilitated. 
Rowland of Baltimore and Higgs of Liverpool have, achieved very 
marked success in photographing the sun's spectrum. The next 
illustration on this page shows a very small part of that spectrum, 
known as the ' Great G group,' highly amplified, from a photograph 



III III 

II! Mi 



III 



!f1i 



lllll 



ll I llll 



43 


11' 

I'fM 



lllllt 

ipiiiiliM 



llll 



\. Ji 



Great G Group of Solar Spectrum (photographed by Higgs) 



by the latter. These lines are in the indigo. Many hundreds of the 
dark lines in the sun's spectrum are caused by absorption in our 
atmosphere. They are called telluric lines, and variation in their 
number and intensity affords an excellent method of finding the 
amount of aqueous vapor in the atmosphere, as Jewell and others 
have shown. 

Elements already recognized in the Sun. — This process 
of comparison of the solar spectrum with spectra of terres- 
trial elements has been carried so far that about 40 of these 
substances are now known to exist in the sun. Among 
them are (according to Rowland and others): — 



(Al) Aluminium 

(Cd) Cadmium 

(Ca) Calcium 

(C) Carbon 

(Cr) Chromium 

(Co) Cobalt 

(Cu) Copper 



(H) Hydrogen 

(Fe) Iron 

(Mg) Magnesium 

(Mn) Manganese 

(Ni) Nickel 

(Sc) Scandium 

(Si) Silicon 



(Ag) Silver 

(Na) Sodium 

(Ti) Titanium 

(V) Vanadium 

(Y) Yttrium 

(Zn) Zinc 

(Zr) Zirconium 



The certainty with which an element is recognized de- 
pends upon two things : {a) the number of coincidences of 
spectral lines, {b) the intensity of the lines. Calcium ranks 
first in intensity, but iron has by far the greatest number 
of lines, with more than 2000 coincidences. All told, it 
may be said that iron, calcium, hydrogen, nickel, and sodium 



The Bolometer 



277 



are the most strongly indicated. Runge has found certain 
evidence of oxygen in the sun. Chlorine and nitrogen, 
abundant elements on the earth, and gold, mercury, phos- 
phorus, and sulphur are not indicated in the solar spectrum. 
Sun-spot Spectrum. — If the spectrum of the sun itself 
is complicated, that of a spot is even more so. In it are 
multitudes of fine dark lines, indicating a greater degree 
of gaseous absorption than prevails on the sun generally. 

A few of the Fraunhofer lines in the ordinary solar spectrum are 
not only deepened in intensity, but broadened out in the spot spectrum, 
as shown in the illustration. The dark belt running lengthwise through 
the middle is the 
spectrum of the 
umbra, and above 
and below it are 
spectra of both 
sides of the pen- 
umbra, much less 
dark. Thickening 
of the lines is most 
marked in the um- 
bra, and gradually 
diminishes on both 
sides to the edges 
of the penumbra. 
Not infrequently 

these heavily thickened lines are pierced in the middle by a narrow 
bright line, called a* double reversal.' Always this is true of the H 
and A" bands in the spot spectrum. Spectra of many spots strengthen 
the view that the spots are themselves depressions. Occasionally it 
happens that there is a violent motion, either toward or from us, of the 
gases above a spot ; this produces in the spectrum a marked distortion 
or branching of the dark lines. By measuring the amount and direc- 
tion of this distortion, it can be calculated whether the gases were 
rushing toward or from us, and at what speed. On rare occasions 
these velocities have been as great as 200 or even 300 miles per second. 
The simple principle by which this is done is known as ' Doppler's 
principle.' It is explained on page 432. 

The Bolometer. — With rise in its temperature, a metal becomes a 
poorer conductor of electricity ; with loss of heat, it conducts elec- 
tricity better. Iron at 300° below centigrade zero is nearly as perfect 




Thickened Lines of Spot Spectrum 



278 



The Sun 



an electrical conductor as copper at ordinary temperatures. Upon the 
application of this important relation depends the principle of the 
bolometer. Its distinctive feature is a tiny strip of platinum leaf, look- 
ing much like a fine hair or coarse spiderweb. It is about \ inch long, 
^Jo inch broad, and so thin that a pile of 25,000 such strips would be 
only an inch high. This bolometer strip is connected into an electric 
circuit, and it is then carried slowly along the region of the infra-red 
spectrum, and kept parallel to the Fraunhofer lines. So sensitive is 
this instrument that the inconceivably slight change of temperature 
of only the one-millionth of a degree of the centigrade scale may be 
indicated. 

Infra-red of the Solar Spectrum. — Beneath and beyond 
the red in the solar spectrum is an extensive region of dark 
bands wholly invisible to the human eye ; nevertheless it 
has been photographed with certainty. But the actinic or 




Invisible Heat Spectrum (photographed by Langley) 



chemical intensity is very feeble in this region, so that it is 
difficult to photograph directly. Langley, by means of an 
ingenious automatic process, in conjunction with his bo- 
lometer, or spectro-bolometer, has photographed the sun's 
heat spectrum in a form comparable with the normal spec- 
trum. The above illustration represents its dark bands. 
The length of the invisible spectrum is extraordinary, being 
10 times that of the sun's luminous spectrum, which would 
be represented on the same scale by a trifle more than the 
diameter of a lead pencil to the left of A. 

Ultra-violet of the Solar Spectrum. — When we pass to higher re- 
gions of the sun's spectrum known as the violet, the light intensity is 
rapidly weakened, so that the lines become invisible to the eye. Pho- 
tographs of this region can, however, be taken, because the chemical 
intensity is great. In this manner, photographic maps of the invisible 



Absorption by Solar Atmosphere 279 

ultra-violet spectrum were made by Cornu, and their length is many 
times that of the visible spectrum. Just v^^here the ultra-violet spectrum 
really ends is not known, as the farther region of it appears to termi- 
nate abruptly in consequence of absorption by the earth's atmosphere. 

How to distinguish True Solar from Telluric Lines. — Dark lines in 
the solar spectrum being produced by absorption in our own atmos- 
phere, as well as in that of the sun, it is important to have some method 
of distinguishing between them. One way is as follows, employing 
Doppler's principle. Arrange the spectroscope so that sunlight may 
fall upon a small oscillating mirror, which reflects into the slit alter- 
nately rays from the east and the west limb. On account of the sun's 
rotation, the east limb is coming toward us ; so the truly solar lines 
in its spectrum will be displaced toward the violet. Similarly, those 
of the west limb will lie toward the red, because that limb is going 
from us. As the mirror oscillates, Fraunhofer lines caused by solar 
absorption will themselves vibrate forth and back, as if the spectrum 
were being shaken ; but dark lines due to absorption by our atmosphere 
will remain all the time immovable — a method due to Cornu. 



Absorption by Solar Atmosphere. — Absorption by the 
sun's own atmosphere not only reduces the amount of sun- 
light received by the earth, but also changes its character. 
Langiey has ascertained 
that if this atmosphere 
possessed no absorbing 
property, the sun would 
shine two or three times 
brighter than it now does, 
and with a bluish color 
resembling that of the 
electric arc Hght. 

Project the sun's entire image 
on a screen, as if looking for 
spots ; quite marked is the dif- 
ference between the intensity 
of light at center of disk and 
at its edge. Try the experi- 
ment illustrated in the adjacent 
picture. Where the sun's image falls upon a screen, puncture it 
in two places, so that two pencils of sunlight may pass through and 




Solar Disk much brighter at the Center 
than near the Linnb 



2 8o The Sun 

fall upon a second screen. As one of these comes from the edge of the 
solar disk, and the other from its center, their diiference in intensity is 
rendered very obvious. It can be measured by a photometer. The 
sun's disk is only two fifths as bright close to the limb as at the center. 
This comparison relates only to rays by which wx see in the red and 
yellow part of the spectrum. If a similar comparison is made for blue 
and violet rays, by which the photographic plate is affected, absorp- 
tion is very much greater ; photographically, the light at the edge of 
the sun's disk is only one seventh as strong as at the center. This 
renders it difficult to photograph the entire sun with but a single expo- 
sure, so as to show an even disk ; for if the exposure is short enough 
for the bright center, the image is very faint at the border. 

The Chromosphere and Prominences. — Above and every- 
where surrounding the sun's bright surface is a gaseous 
envelope, called the chromosphere. First seen during the 
total solar eclipses of 1605 and 1706 as an irregular rose- 
tinted fringe, analysis of the light shows that it is mainly 
composed of glowing hydrogen, although sodium, magne- 
sium, and other metals are present. Depth of the chromo- 
sphere is not everywhere the same, and it varies between 
5000 and 10,000 miles. Projected up through the chromo- 
sphere, but connected with it, are the fiery-red, cloud- 
shaped prominences or protuberances. It was first found 
that they are not lunar appendages, because the moon was 
seen to pass gradually over them during a total eclipse. 
Afterward the spectroscope verified this inference by 
showing that their light is due chiefly to incandescent 
hydrogen. Also there are the H and K lines, indicating 
vapor of calcium ; and a bright yellow line, Z^g, due to 
helium, an element not known on the earth till discovered 
in 1895 by Ramsay, but long known by its line to 
exist in the sun, whence its name. It is a very light gas 
obtained from a mineral called uraninite. The promi- 
nences are now photographed every clear day by means 
of the spectroheliograph. This ingenious instrument fur- 
nishes in a few seconds a complete picture of the promi- 



The Spectroheliograph 



281 



nences all the way round the sun's limb, which by the 
older methods of observing the protuberances piecemeal 
would require hours to make. Prominences cannot be 
observed by the telescope alone without the spectroscope, 
except during eclipses of the sun. They are most abun- 
dant over the sun's equator and the zones of greatest 
spottedness on either side of it ; but while spots are never 
seen beyond latitude 
45°, prominences 
have been observed 
in all latitudes, even 
up to the sun's poles. 
They are least nu- 
merous about latitude 

65°. 

The Spectroheliograph. 
— Young in 1870 was the 
first to photograph a solar 
prominence. No very 
decided success was at- 
tained until about 20 years 
afterwards, by the use of 
sensitive dry plates ex- 
posed in the spectroscope. 
By the addition of suit- 
able accessory apparatus — 
mainly a second slit with 
the means of moving 
both slits automatically, — 
the spectroscope is con- 
verted into a spectrohelio- 
graph. This remarkable 

instrument, as devised and employed by Hale and built by Brashear, 
is depicted in the above illustration. On page's 282 and 283 are photo- 
graphs of two large prominences, taken with the spectroheliograph. 
By occulting the sun's disk behind an opaque circular screen just large 
enough to cover it and permit the light of the chromosphere to graze its 
edge, all the prominences and the entire chromosphere are photo- 
graphed at once. Records of this character are now rapidly accumu- 




The Spectroheliograph i,Hale> 



282 The Sun 

lating, day by day. Having made exposure for chromosphere and 
prominences, if the occulting disk is then removed, and the sHt made 
to travel swiftly back, the photograph comes out as already shown on 
page 269, in which the faculae are especially prominent. A similar in- 
strument with which almost identical results are obtained has been 
devised and used by Deslandres of the Paris Observatory. 

Classification of the Prominences. — The number, height, 
and variety of forms of prominences are very great. 
They are seen at every part of the sun's limb, being most 
abundant in an equatorial zone about 90° in breadth. Be- 




Eruptive Prominence (25th March, 1895). Spectroheliogram by Hale 

yond latitude 45° north and south, there is a marked fall- 
ing off to about 65°, followed by a renewed frequency in 
the region of both poles. The average height of the 
prominences is about 25,000 miles, or about three times 
the diameter of the earth. Occasionally prominences start 
up to a height exceeding 100,000 miles, as indicated on the 
colored plate at page 10; and the greatest heights ever 
observed were 300,000 and 350,000 miles, approaching half 
the sun's diameter. The latter was observed by Young, 
7th October, 1880. Frequently protuberances are promi- 
nently developed at exactly opposite points on the sun's 




I 



u 

"^ 

w 

o 

< 
o 

C/5 






The Envelopes of the Sun 



283 



disk. As to form and structure, prominences are divided 
into two classes : eruptive or metallic, and cloud-like, qui- 
escent prominences of hydrogen (see plate v). The 
former generally appear like brilliant jets, or separate 
filaments, varying rapidly in form and brightness. The 
spectrum of eruptive prominences shows the presence of a 
large number of metallic vapors. For the most part they 
are observed near the spot zones only, and never very near 




Quiescent Prominence (3d July, 1894). Spectroheliogram by Hale 

the poles of the sun. The velocity of detached filaments 
often exceeds lOO miles in a second of time, and on rare 
occasions it is four or five times as swift. Frequently 
prominences form exactly over spots. Quiescent ones are 
usually of enormous size laterally, and in appearance they 
are a close counterpart of terrestrial cirrus and stratus 
clouds. Changes in them are not as a rule rapid, and near 
the sun's poles they have been known to last nearly a month 
without much change of form. Tacchini of Rome has been 
the most persistent observer of prominences. 

The Envelopes of the Sun. — The interior of the sun is 



284 



The Sun 



probably composed of gases, in a state quite unfamiliar to 
us, on account of intense heat and compression due to solar 
gravity. In consistency they may perhaps resemble tar or 
pitch. A series of layers, or shells, or atmospheres sur- 
round the main body of the sun. The illustration has been 
conceived by Trouvelot to show the condition of things 
at the sun's surface and just beneath it. Although the 
view is a theoretical one, it has been made up from a rea- 




Atmosphere of the Sun in Ideal Section (from Bulletin Astronomique) 



sonable interpretation of all the facts. Proceeding from 
the outside inward, we meet first the very thin shell called 
the chromosphere, probably about 5000 miles in thickness. 
Immediately underneath is the photosphere, made up of 
filaments due to the condensation of metallic vapors. The 
outer ends of these filaments form the granular structures 
which we see upon the sun generally, and their light shines 
through the chromosphere. Between them and the chromo- 
sphere is an envelope thinner still, perhaps looo miles in 
thickness, and represented by the darker shaded upper 
side of the photosphere. It is called the reversing layer. 
In this gaseous envelope takes place that absorption which 
gives rise to the Fraunhofer lines. Where undisturbed by. 
eruptions from beneath, the filaments of the photosphere 
are radial ; but where such eruptions take place, producing 
under certain conditions the spots, these filaments are 



Light a7id Brilliance of the Sun 285 

swept out of their normal vertical lines, as shown, form- 
ing the penumbra of the spot as seen from our point of 
view. From the outer surface of the body of the sun 
proper (w^hich we never see) rise vapors of hydrogen and 
various metals of which the sun is composed. Numerous 
of these eruptive columns are shown. They are spread 
into masses of cloud-like forms composed of metallic vapors 
underneath the photosphere. As these columns grow 
in number and stress becomes more and more intense, 
outbursts through the photospheric shell take place, giv- 
ing rise to phenomena known as sun spots and protuber- 
ances. Naturally such eruptions would be more violent at 
one time than at another, and we might expect them to 
occur periodically, just as we observe the spots actually 
do. Still above the chromosphere and prominences is the 
corona, not an atmosphere, properly speaking, but a lumi- 
nous appendage of the sun (not shown in this illustration) 
whose light is of a complex character, and about which 
relatively little is known, because it can be seen only dur- 
ing total ecHpses of the sun. Illustrations of it are given 
in the next chapter, with theories of its constitution. 

Light and Brilliance of the Sun. — It is not easy to con- 
vey, in words or figures, any idea of the amount of light 
given out by the sun, since the figures expressed in ' candle 
power,' or in terms of the ordinary gas burner, or even the 
arc light, are so enormous as really to be beyond our com- 
prehension. Indeed, any of these artificial illuminations, 
even the most brilliant electric light, if placed between the 
eye and the sun, seems black by comparison. The sun is 
nearly four times brighter than the brightest part of the 
electric arc. By an experiment at a steel works in Penn- 
sylvania, Langley compared direct sunlight with the blind- 
ing stream of molten metal from a Bessemer converter ; and 
although absolutely dazzling in its brightness, sunlight 



286 The Sun 

was found to be more than 5000 times brighter. The 
amount of hght received from the sun is equal to that from 
600,000 full moons. 

The Sun's Heat at the Earth. — Although difficult to give 
an idea of the sun's light, much more so is it to convey an 
adequate notion of his enormous heat. So great is that 
heat, even at our vast distance from the sun, that it exceeds 
intelligible calculation. The unit of heat is called the calorie, 
and it signifies the amount of heat required to raise the tem- 
perature of a kilogram of water one degree of the centi- 
grade scale. The number of calories received each minute 
upon a square meter of the earth's surface has been re- 
peatedly measured, and found to be 30, neglecting the 
considerable portion which is absorbed by our atmosphere. 
No variation in this amount has yet been detected ; so that 
30 calories per square meter per minute is termed the solar 
constant. With the sun in the zenith, his heat is powerful 
enough to melt annually a layer of ice on the earth nearly 
170 feet in thickness. Or if we measure off a space five 
feet square, the energy of the sun's rays, when falling ver- 
tically upon it, is equivalent to one horse power, or the 
work of about five men. Upon the deck of a steamer on 
tropical oceans there falls enough heat to propel it at about 
10 knots, if only that heat could be fully utilized. Several 
attempts have been made to employ solar heat directly for 
industrial purposes, and Ericsson, the great Swedish engi- 
neer, and Mouchot built solar engines. The sun's gaseous 
envelope, too, absorbs heat. Frost has shown that all 
parts of the disk radiate uniformly, and that we should 
receive 1.7 times more heat, if the solar atmosphere were 
removed. 

The Sun's Heat at the Sun. — The intensity of heat, 
like that of light, decreases as the square of the distance 
from the radiating body increases. Therefore, the amount 



Maintenance of Solar Heat 287 

of heat radiated by a given area of the sun's surface must 
be about 46,000 times greater than that received by an 
equal area at the distance of the earth. 

One square meter of that surface radiates heat enough to generate 
more than locooo horse power, continuously, night and day. Imagine 
a solid cylinder of ice, nearly three miles in diameter and as long as the 
distance from the earth to the sun. The sun emits heat sufficient to 
melt this vast column in a single second of time ; in eight seconds it 
would be converted into steam. Were the sun no farther from us than 
the moon, not only w^ould his vast globe fill the entire sky, but his over- 
powering heat would vaporize the oceans, and speedily melt the solid 
earth itself. To investigate this inconceivable outlay of heat, to deter- 
mine the laws of its radiation and its effects upon the earth, and to 
theorize upon the method by which this heat is maintained, are among 
the most important and practical problems of the astronomy of the 
present day. Whether the amount of heat given out by the sun is a 
constant quantity, or whether it varies from year to year or from cen- 
tury to century, is not yet determined. The temperature of the sun is 
very difficult to ascertain. Widely different estimates have been made. 
Probably 16,000^ to 18,000^ Fahrenheit is near the truth. But no 
artificial heat exceeds 4000^ F. 

How the Sun's Heat is maintained. — The sun's heat 
cannot be maintained by the combustion of carbon, for 
although the vast globe were solid anthracite, in less than 
5000 years it would be burned to a cinder. Heat, we 
know, may result from sudden impact, as the collision 
of bodies. According to one theory, the sun's heat may be 
maintained by the impact of falling meteoric matter, and 
very probably this accounts for a small fraction ; but in 
order that all the heat should be produced in this manner, 
an amount of matter equal to a -hundredth part of the 
earth's mass would have to fall upon the sun each year 
from the present distance of the earth. This seems very 
unlikely. Only one possible explanation remains : if the 
sun is contracting upon himself, no matter how slowly, 
gases composing his volume must generate heat in the 
process. The eminent German physicist, von Helmholtz 



288 The Sun 

first proposed this theory, nearly a half century ago, and 
it is now universally accepted. So enormous is the sun 
that the actual shortening of his diameter (the only dimen- 
sion we can measure) need take place but very slowly. In 
fact, a contraction of only six miles per century would fully 
account for all the heat given out by the sun. But six 
miles would subtend an angle of only y^g- of a second 
of arc at the sun, and this is very near the limit of 
measurement with the most refined instruments. So it is 
evident that many centuries must elapse before observa- 
tion can verify this theory. 

The Past and Future of the Sun. — Accepting the 
theory that the sun's heat is maintained by gradual 
shrinkage of his volume, he must have been vastly larger 
in the remote past, and he will become very much reduced 
in size in the distant future. If we assume the rate of 
contraction to remain unchanged through indefinite ages, 
it is possible to calculate that the earth has been receiving 
heat from the sun about 20,000,000 years in the past; 
also, that in the next 5,000,000 years, he will have shrunk 
to one half his present diameter. For 5,000,000 years addi- 
tional, he might continue to emit heat sufficient to main- 
tain certain types of life on our earth. A vast periodof 
30,000,000 to 40,000,000 years, then, may be regarded as 
the likely duration, or life period, of the solar system, from 
origin to end. Their heat all lost by radiation, the sun 
and his family of planets might continue their journey 
through interstellar space as inert matter for additional 
and indefinite millions of years. 



CHAPTER XII 

ECLIPSES OF SUN AND MOON 

IN earliest ages, every natural event was a mystery. 
Day and night, summer and winter, and the most 
ordinary occurrences filled whole nations with wonder, 
and fantastic explanations were given of the simplest 
natural phenomena. But when anything happened so 
strange, and even frightful, as the total darkening of the 
sun in the daytime, it is scarcely matter for surprise that 
fear and superstition ran riot. Some nations believed 
that a vast monster was devouring the friendly sun, and 
barbarous noises w^ere made to frighten him aw^ay. For 
ages the sun was an object of worship, and it was but 
natural that his darkening, apparently inexplicable, should 
have brought consternation to all beholders. Among 
uncivilized peoples, the ancient view regarding eclipses 
prevails to the present day. 

Remarkable Ancient Eclipses. — The earliest mentioned solar eclipse 
took place in B.C. 776, and is recorded in the Chinese annals. During 
the next hundred years several eclipses were recorded on Assyrian tab- 
lets or monuments. On 28th May, B.C. 585, took place a total eclipse 
of the sun, said to have been predicted by Thales, which terminated a 
battle between the Medes and Lydians. This eclipse has helped to 
fix the chronology of this epoch. So, too, a like eclipse, 3d August, 
B.C. 431, has established the epoch of the first year of the Peloponnesian 
war; and the eclipse of 15th August, B.C. 310, is historically known as 
^ the eclipse of Agathocles,' because it took place the day after he had 
invaded the African territory of the Carthaginians, who had blockaded 
him in Syracuse : ^ the day turned into night, and the stars came out 
everywhere in the sky.' Also a few solar eclipses are connected with 

TODD'S ASTRON. — I9 289 



290 



Eclipses of Sun mid Moon 



events in Roman history. The first historic reference to the corona, 
or halo of silvery light which seems to encircle the dark eclipsing moon, 
occurs in Plutarch's description of the total eclipse of 20th March, a.d. 
71. Although it must have been frequently seen, there is no subsequent 
mention of it till near the end of the i6th century. The few eclipses 
recorded in this long interval have little value, scientific or otherwise, 
except as they have helped modern astronomers to ascertain the motion 
of the moon. 



X THE SUN 



The Cause of Solar Eclipses. — Any opaque object inter- 
posed between the eye and the sun will cause a solar 

ecHpse ; and it will 
be total provided the 
angle filled by the 
object is at least as 
great as that which 
the sun itself sub- 
tends ; that is, about 
one half a degree. 
Every one recog- 
nizes the shadow of 
the eagle flying over 
the highway, and the 
cloud's dark shadow 
moving slow^ly across 
the landscape, as pro- 
duced by the inter- 
position of a dark 
body between sun 
and earth. To the 
eager spectators on 
the towers of Notre 
Dame, Paris, 21st 
October, 1783, there 
appeared a novel sort of solar eclipse, caused by the drift- 
ing between them and the sun of the balloon in which 



■»■"" 



EARTH 




How Eclipses of Sun and Moon take Place 



Shadows of Heavenly Bodies 



291 



were M. Pilatre and the Marquis 
d'Arlandes. And just as when the 
eye is placed below the eagle, or 
behind the cloud, or beneath the 
balloon, an apparent but terrestrial 
eclipse of the sun is seen, just so 
when the moon comes round be- 
tween earth and sun a real or astro- 
nomical eclipse of the sun takes 
place. But the great advantage of 
the latter comes from the fact that 
the moon, the eclipse-producing 
body, is very much farther away 
than cloud, and eagle, and balloon 
are, — beyond the atmosphere of the 
earth, at a distance relatively very 
great and comparable with that of 
the sun itself. It is a striking fact 
that the sun, about 400 times larger 
than the moon, happens to be about 
400 times farther away, so that sun 
and moon both appear to be of 
nearly the same size in the heavens. 
A slight variation of our satellite's 
size or distance might have made that 
impressive phenomenon, the sun's 
total eclipse, forever impossible. 

The Shadows of Heavenly Bodies. 
— As every earthly, object, when in 
sunshine, casts a shadow of the 
same general shape as itself, so do 
the celestial bodies of our solar sys- 
tem. All these, whether planets or 
satellites, are spherical ; and as they 



^^^ t 



to 



s 



°^%-... 



^^<o. 



%'s 



o'^y 



;^5''' 



I 



Slender Shadows of Earth 
and Moon 



292 Eclipses of Sun and Moon 

are smaller than the sun, it is evident that their shadows 
are long, narrow cones stretching into space and always 
away from that central luminary. Evidently, also, the 
length of such a shadow depends upon two things, — the 
size of the sphere casting it, and its distance from the 
sun. The average length of the shadow of the earth is 
857,000 miles; of the moon, 232,000 miles. Each is at 
times about -^-^ part longer or shorter than these mean 
values, because our distance from the sun varies -^-^ part 
from the mean distance. So far away is the sun that the 
shadows of earth and moon are exceedinsflv Ions: and 
slender. To represent them in their true proportions is 
impossible within the limits of a small page like this. In 
the illustration just given, however, attempt is made to 
give some idea of these slender shadows ; but even there 
they are drawn five times too broad for their length. The 
shadow cast by a heavenly body is a cone, and is often 
called the umbra, or dense shadow, because the sun's light 
is w^holly withdrawn from it. Completely surrounding the 
umbra is a less dense shadow, from which, as the figure 
on page 290 shows, the sun's light is only partly excluded. 
This is called the penumbra ; and it is a hollow frustum 
of a cone, whose base is turned opposite to the base of the 
umbra. Both umbra and penumbra sweep through space 
with a velocity exceeding 2000 miles an hour; and they 
trail eastward across our globe. The way in which they 
strike its surface gives rise to different kinds of solar 
eclipse, known as partial, annular, and total. 

True Proportions of Earth^s and Moon^s Orbits. — Even more difficult 
is it to represent the sizes and distances of sun. earth, and moon, in their 
true relative proportions on paper. It is easy, however, to exhibit them 
correctly in a medium-sized lot. Cut out a disk one foot in diameter to 
represent the sun. Pace off 107 feet from it, and there place an ordi- 
nar\' shot, yV i^ch in diameter, to represent the earth. At a distance of 
3^ inches from the shot, place a grain of sand, or a very small shot, to 



Abodes of Lunar Orbit 



293 




represent, the moon. Then not only will the sizes of sun. earth, and 
moon, be exhibited in true proportion, but the dimensions of earth's and 
moon's orbits will be correctly indicated on the 
same scale. Every inch of this scale corre- 
sponds to 72,000 miles in space. 

The Nodes of the Moon's Orbit. — 

Once every month — that is, every time 

the moon comes to the phase called 

new — there would be an eclipse of the 

sun, were it not that the moon's path 

about the earth, and that of the earth 

about the sun are not in the same plane, 

but inclined to each other by an angle 

of 5^°. When our satellite comes round 

to conjunction or new moon, she usually 

passes above or below the sun, which ^Zr^^^^l^L:^^^^ 

therefore suffers no eclipse. Two 

opposite points on the celestial sphere where the plane of 

moon's orbit crosses ecliptic are called the moon's nodes. 

Indeed, the term ecliptic had its 
origin from this condition : it is 
the plane near to which the moon 
must be in order that eclipses 
shall be possible. 

The figures should make this clear. 
The sun is w^here the eye is, and the 
disk held at arm's length represents the 
lunar orbit, the earth being at its center. 
When held at the side, with the wrist 
bent forward, the moon's shadow falls 
far below the earth, and an eclipse is 
impossible. Now carry the disk slowly 
to the position of the second figure, 
gradually straightening out the wrist, 
and taking care to keep plane of disk 
always parallel to its first position : moon's orbit is now seen edge on, 
and when new moon occurs, an eclipse of the sun is inevitable. 




Sun in Plane of Moon's Orbit - 
Eclipses Inevitable 



294 Eclipses of Sujt a7id Moon 

Solar Ecliptic Limit. — As a solar eclipse cannot take place unless 
some part of the moon overlaps the sun's disk, it is clear that the 
apparent diameters of these two bodies must affect the distance of the 
sun from the moon's node, within which an eclipse is possible. This 
distance is called the solar ecliptic limit, and the figure illustrates it on 
both sides of the ascending node. From the new moon at the center 
to the farther new^ moon on either side is an arc of the ecliptic about 
1 8° long. This is the value of the solar ecliptic limit. It is not a con- 
stant quantity, but is greatest when perigee and perihelion occur at the 

NO ECLIPSE ~ 

PARTIAL ECLIPSE ANNULAR OR 

TOTAL ECLIPSE PARTIAL ECLIPSE NO ECLIPSE 

ECLIPTIC 



-IPTIG 

NEWMOON^^ MooiNM^ 

NELW MOON 

Solar Ecliptic Limit, both East and West of Moon's Ascending Node 

same time. As our satellite may reach the new-moon phase at any 
time wdthin this limit, and may therefore eclipse the sun at any dis- 
tance less than i8^ from the moon's node, all degrees of solar eclipse 
are possible. They will range from the merest notch cut out of the 
sun's disk when he is remote from the node, to the central (annular 
or total) eclipse when he is very near the node. 

Two Solar Eclipses Certain Every Year. — As the solar 
ecliptic limit is i8° on both sides of the moon's node, it is 
plain that an eclipse of the sun of greater or less magni- 
tude is inevitable at each node, every year. For the 
entire arc of possible eclipse is about 36°, and the sun 
requires nearly 37 days to pass over it. If, therefore, new 
moon occurs just outside of the limit west of the node (as 
on the right in the figure just given), in 29^ days she will 
have made her entire circuit of the sky, and returned to 
the sun. An eclipse (partial) at this new moon is certain, 
because the sun can have advanced only a few degrees 
east of the node, and is well within the limit. One solar 
eclipse is therefore certain at each node every year. 

If new moon falls just within the limit west of the node, two partial 
solar echpses are certain at that node ; also two are possible in like 
manner at the opposite node. Even a fifth solar eclipse in a calendar 



Partial Solar Eclipses 



295 



year may take place in extreme cases. For if the sun passes a node 
about the middle of January, causing two eclipses then, two may also 
happen in midsummer; and the westward motion of the node makes 
the sun come again within the west limit in the month of December, 
with a possibility of a fifth solar eclipse before the calendar year is out. 
As two lunar eclipses also are certain in this period, the greatest possi- 
ble number of eclipses in a year is seven. But this happens only once 
in about three centuries, the next occasion being the year 1935. The 
number of echpses in a year is commonly four or five. 

Partial Solar Eclipses. — When the moon comes almost 
between us and the sun, she cuts off only a part of the 
solar light, and a partial eclipse takes place. 




Exposure of 
the viiniimim 
phase iinme- 
diately above 
was too lo7ig 
and the nega- 
tive was so- 
larized 



Solar Eclipse of 1887 (photographed in Tokyo, Japan) 



This happens when the sun is some distance removed from the node 
of the lunar orbit. The above figures, i to 14, show several advanc- 
ing and retreating stages of a partial eclipse. The degree of obscura- 
tion is often expressed by digits, a digit being the twelfth part of the 
sun's diameter. When there is a partial eclipse, it is only the moon's 
penumbra which strikes the earth, consequently the partial eclipse will 
be visible in greater or less degree from a large area of the earth's sur- 
face, perhaps 2000 miles in breadth, if measured at right angles to the 
shadow, but often double that width on the curving surface of our 



296 



Eclipses of Sun and Moon 




Annular Eclipse 



globe. This will be near the north pole or the 
south pole according as the center of the moon 
passes to the north or south of the center of the 
sun. About 90 partial eclipses of the sun occur in 
a century. 

Annular Eclipses. — If the sun is very 
near the moon's node when our satelHte 
becomes new, clearly the moon must then 
pass almost exactly between earth and 
sun. If at the same time she is in apogee, 
her apparent size is a little less than that 
of the sun. Then her conical shadow 
does not quite reach the surface of the 
earth, and a ring of sunlight is left, sur- 
rounding the dark moon completely. This 

is called an annular eclipse because of the annulus, or 

bright ring of sunlight still left shining. 



Its greatest possible breadth 
is about 2V the sun's apparent 
diameter. This ring may last 
nearly \2\ minutes under the 
most favorable circumstances, 
though its average duration is 
about one third of that inter- 
val . The illustration shows the 
ring at five different phases. 
Nearly 90 annular eclipses of 
the sun take place every cen- 
tury. Dates of annular eclipses 
near the present time are : — 

1897, July 29, visible in 
Mexico, Cuba, and Antigua. 

1900, November 22, from 
Angola to Zambesi and West 
Australia. 

No annular eclipse visits 
the United States till 28th 



June, 1 908, when one may be ^, r .1. a , / ^ ^ r t^ 

w ' Tr^ 'A Phases of the Annulus Treduced from a Da^erreo- 




well seen in Florida. 



type by Alexander) 



Total Solar Eclipses 



297 



Total Solar Eclipses. — Most impressive and important 
of all obscurations of heavenly bodies is a total eclipse of 
the sun. It takes place when the lunar shadow actually 
reaches the earth as in the illustration. While the moon 
passes eastward, approaching gradually the point where 
she is exactly between us and the sun, steadily the dark- 
ness deepens for over an hour, as more and more sun- 
light is withdrawn. Then quite suddenly the darkness of 
late twilight comes on, when the moon 
reaches just the point where she first shuts 
off completely the light of the sun. At 
that instant, the solar corona flashes out, 
and the total eclipse begins. The observer 
is then inside the umbra, and totality lasts 
only so long as he remains within it 
Total eclipses are sometimes so dark that 
observers need artificial light in making 
their records. In consequence of the mo- 
tion of the moon, the tip of the lunar 
shadow, or umbra, makes a path or trail 
across the earth, and its average breadth 
is about 90 miles. The earth by its rota- 
tion is carrying the observer eastward in 
the same direction that the shadow is going. If he is 
within the tropics, his own velocity is nearly half as great 
as that of the shadow, so that it sweeps over him at can- 
non-ball speed, never less than 1000 miles an hour. As an 
average, the umbra will require less than three minutes to 
pass by any one place, but the extreme length of a total 
solar eclipse is very nearly eight minutes. Few have, 
however, been observed to exceed five minutes in duration ; 
and no eclipses closely approaching the maximum duration 
occur during the next 2\ centuries. Total eclipses occur- 
ring near the middle of the year are longest, if at the 




Total Eclipse 



298 Eclipses of Sun and Moon 

same time the moon is near perigee, and their paths fall 
within the tropics. Always after total eclipse is over, the 
partial phase begins again, growing smaller and smaller 
and the sun getting continually brighter, until last contact 
when full sunlight has returned. Nearly 70 total eclipses 
of the sun take place every century. If the atmosphere 
is saturate with aqueous vapor, w^eird color effects ensue, 
by no means overdrawn in the frontispiece. 

The Four Contacts. — As the moon by her motion eastward overtakes 
the sun, an eclipse of the sun ahvays begins on the west side of the 
solar disk. First contact occurs just before the dark moon is seen to 
begin overlapping the sun's edge or limb. Theoretically the absolute 
first contact can never be observed ; because the instant of true contact 
has passed, a fraction of a second before the moon's edge can be seen. 
First contact marks the beginning of partial eclipse. If the eclipse is 
total or annular, a long partial eclipse precedes the total or annular phase. 
At the instant this partial eclipse ends, the total or annular eclipse 
begins; and this is the time when second contact occurs. Usually 
second contact will follow first contact by a little more than an hour. 
If the eclipse is total, second contact takes place on the east side of the 
sun ; if annular, on the west side. Following second contact, by a very 
few moments at the most, comes third contact : in the total eclipse, it 
occurs at the sun's west limb ; in the annular eclipse, at the east limb. 
Students should represent the contacts by a diagram. Then from third 
contact to last contact is a partial eclipse, again a little more than an 
hour in duration — the counterpart of the partial eclipse between first 
and second contacts. Fourth or last contact takes place at the instant 
when the moon's dark body is just leaving the sun, and the interval be- 
tween first and fourth contacts is usually about 3 hours. If the eclipse 
is but partial, only tw^o contacts, first and last, are possible. 

Young's Reversing Layer. — According to the principles 
of spectrum analysis, a gas under low pressure gives a 
discontinuous spectrum composed of characteristic bright 
lines. As the dark lines of the solar spectrum are produced 
by absorption in passing through the atmosphere of the 
sun, it occurred to Young that a total eclipse afforded an 
opportunity to observe the bright-line spectrum of this 
atmosphere by itself. Following is his description of this 



The Solar Corona 299 

phenomenon, as seen for the first tune in Spain, during 
the total eclipse of 1870: — 

^ As the moon advances, making narrower and narrower the remaining 
sickle of the solar disk, the dark Unes of the spectrum for the most part 
remain sensibly unchanged. . . . But the moment the sun is hidden, 
through the wliole length of the spectrum, in the red, the green, the 
violet, the bright lines flash out by hundreds and thousands, almost 
startlingly ; as suddenly as stars from a bursting rocket head, and as 
evanescent, for the whole thing is over within two or three seconds. The 
layer seems to be only something under a thousand miles in thickness.' 
A like observation has been made on several occasions, and during the 
totality of 1896 the bright lines were successfully photographed. This 
stratuiu of the solar atmosphere, known as Young's reversing layer, 
is probably between 500 and 1000 miles in thickness. 

The Solar Corona. — The corona is a luminous radiance 
seen to surround the sun during total eclipses. The strong 
illumination of our atmosphere precludes our seeing it at 
all other times. The corona, as observed with the tele- 
scope, is composed of a multitude of streamers or filaments, 
often sharply defined, and sometimes stretching out into 
space from the disk of the sun millions of miles in length. 
For the most part these streamers are not arranged radially, 
and often the space between them is dark, close down to 
the disk itself. The general light of the corona averages 
about three times that of the full moon ; but the amount of 
this light varies from one eclipse to another, just as the 
form and dimensions of the streamers do. The coronal 
light, very intense close to the sun, diminishes rapidly out- 
ward from the disk, so that the object is a very difficult 
one to photograph distinctly in every part on a single 
plate. The corona appears to be at least triple ; there are 
polar rays nearly straight, inner equatorial rays sharply 
curved, and often outer equatorial streamers, perhaps con- 
nected in origin with the zodiacal light. The last are not 
visible at every eclipse, and it is doubtful whether they 



;oo 



Eclipses of Sun and Moon 



have ever been photographed, although repeatedly seen. 
Recent photographs of the corona show no variation in 
form from hour to hour. As yet no theory of this 
marvelous object explains the phenomena satisfactorily. 
Neither a magnetic theory advanced by Bigelovv, nor a 
mechanical one by Schaeberle, has successfully predicted 
its general form. The brighter filaments may be due to 
electric discharges. Total eclipses permit only a few 
hours' advantageous study of the corona, in a century. 

The Spectrum of the Corona. — Our slight knowledge of 
the. corona is for the most part based on evidence fur- 
nished by the spectroscope. 



Its light gives a faint continuous spectrum, showing incandescent 
liquid or solid matter; and a superposed spectrum of numerous bright 
lines indicating luminous gases, among them hydrogen. Also, in the 
violet and ultra-violet are numerous bright lines. But the characteristic 

hne of the coronal spectrum 
is a bright double one in the 
green, often called the * 1474 
line * ; one component of it 
coincides in position with a 
dark iron line in the solar 
spectrum, and the other is due 
to a supposed element called 
• coronium ' existing in a gase- 
ous form in the corona, but 
as yet unrecognized on the 
earth. Also there are dark 
lines, indicating much reflected 
sunlight, possibly coming from 
meteoric matter surrounding 
the sun. Deslandres, by pho- 
tographing on a single plate 
the spectrum of the corona on 
opposite sides of the sun. obtained a displacement of its bright line, 
showing that eastern filaments are approaching the earth, and western 
receding from it ; and the calculated velocities indicate that the corona 
revolves wdth the sun. Independent proof of the solar origin of the 
corona is thus afforded. 




Corona of 1871 (Lord Lindsay; 



Periodicity of the Corona 



301 




Corona of 1882 (.Schuster and Wesley) 



Periodicity of the Corona. — At no two eclipses of the 
sun is the corona alike. How rapidly it varies is not yet 
found out, but observa- 
tions of the total eclipse 
of 1893 showed that the 
corona was exactly the 
same in Africa as when 
photographed in Chile 
2\ hours earlier. Slow 
periodic variations are 
known to take place, 
seeming to follow the 
I i-year cycle of the spots 
on the sun. At the time 
of maximum spots, the 
corona is made up of an 
abundance of short, bright, and interwoven streamers, 
rather fully developed all around the sun, as in these 

three photographs (India 
1871, Egypt 1882, and 
Africa 1893). At or near 
the sun-spot minimum, 
on the other hand, the 
corona is unevenly de- 
veloped : there are beau- 
tiful, short, tufted 
streamers around the 
solar poles, and outward 
along the ecliptic extend 
the streamers, millions 
of miles in length, as 
pictured in the photo- 
graphs (next page) of total eclipses in the United States in 
1878 and 1889. If a similar form is repeated in the eclipse 




Corona of 1893 ^Deslandres) 



302 



Eclipses of Sun and Moon 




Corona of 1878 (Harkness) 



of 1900, the cycle will be established ; but no sufficient expla- 
nation of this periodicity of the corona has yet been given. 

Important Modern 
Eclipses of the Sun, — 

Not until the European 
eclipse of 1842 did the 
true significance of cir- 
cumsolar phenomena 
begin to be appreciated. 
In the eclipses of 1851 
and i860 it was proved 
that prominences and 
corona belong to the sun, 
and not to the moon. 
Just after the eclipse of 
1868 (India) was made 

the important discovery that prominences can be observed 

at any time without an eclipse by means of the spectro- 
scope. In 1869 (United 

States), bright lines were 

found in the spectrum of 

the corona, one line in 

the green showing the 

presence of an element 

not yet known on the 

earth, and hence called 

coroniitm. In 1870 

(Spain), the reversing 

layer was discovered, and 

in 1878 (United States), 

a vast extension of the 

1 ^ 1 ^ Corona of 1889 (Pritchett) 

coronal streamers about 

1 1 million miles both east and west of the sun (shown 

above only in part). In 1882 (Egypt), the spectrum of the 




The Next Total Eclipse 



303 



corona was photographed for the first time ; and in 1889 
(CaHfornia), exceedingly fine detail photographs of the 
corona were obtained. In 1893 (Africa), it was shown 
that the corona rotates on its axis bodily with the sun ; 
and in 1896 (Nova Zembla), actual spectrum photographs 
of the reversing layer established its existence conclusively. 

A Total Eclipse near at Hand. — The total eclipse of the sun on 
28th May, 1900, occurring in this part of the world and in the early 
future, a map of its path across the Southern States is given below. 







Path of Total Eclipse of 28th May, 1900, through the Southern States 



The central line stretches from New Orleans to Raleigh, both these 
places being very near the middle of the path. The average width 
of the eclipse track, or region within which the eclipse will be total, 
is 55 -miles. Along the central line the duration of total eclipse varies, 
from I m. 15 s. in Louisiana to i m. 45 s. in North CaroHna. Along 
the lines m.arked 'Northern and Southern Limits of Total Eclipse,' 
the sun will remain totally obscured for only an instant. At points in- 
termediate between the central line and either the northern or south- 
ern limits, the length of totality will vary between its duration on the 
central line and os. on the limiting lines themselves. The total phase 
in this region will take place between, half-past seven in the morning, 
at New Orleans, and ten minutes before nine at Norfolk ; and nearly 
a half hour of absolute time will elaose while the moon's shadow is 



304 



Eclipses of Sun and Moon 



traveling across this part of the United States. After leaving Virginia, 
it sweeps over the Atlantic Ocean, and southeasterly across Portugal, 
Spain, and northern Africa. 

Important Future Eclipses. — Total eclipses of the sun 
in the coming quarter century are for the most part visible 
in foreign lands. The paths of only two cross the United 
States. Following are dates of the more important future 
eclipses, regions of general visibility, and approximate 
duration of the total phase : — 



1898, January 22 

1900, May 28 

1901, May 18 
1905, August 30 
1907, January 14 
1912, October 10 
1 9 14, August 21 

1 91 6, February 3 
1918, June 8 



East Africa and India 2 min. 

Louisiana to Virginia 2 '' 

Sumatra, Borneo, and Celebes 6 ^'' 

Labrador, Spain, and Egypt 4 " 

Russia and China 2 " 

Colombia and Brazil i " 

Norway, Sweden, and Russia 2 " 

Northern South America 2 " 

Oregon to Florida 2 " 



Exact times and circumstances of all these eclipses are 
regularly published in the Nautical Almanac, issued by the 




Earth's Shadow and Penumbra in Section 



English, German, French, and American governments, 
two or three years in advance. No total eclipse will be 



Ltiuar Eclipses 



305 



visible in New England or the Middle States till 24th Jan- 
uary, 1925, when the track of one will pass near Portland, 
Maine. The great total eclipses of 1955 (India), and 1973 
(Africa) w411 exceed 7 minutes in duration, the longest for 
a thousand years. 

Eclipses of the Moon. — As all dark celestial bodies cast 
long, conical shadows in space, any non-luminous body 
passing into the shadow of another is necessarily darkened 
or eclipsed thereby. When, in her journey round our earth, 
the moon comes exactly opposite the sun, or nearly so, she 





Lunar Eclipse of 10| Digits 



Lunar Eclipse one Digit short of Totality 



passes through our shadow. Then a lunar eclipse takes 
place. Refer to illustrations given on pages 290 and 291 : 
clearly, a lunar eclipse can happen only when the moon 
is full, or at opposition. There is not an eclipse of the 
moon every month, because unless she is near the plane 
of the ecliptic, that is, near her node at the time, she 
will pass above or below the earth's shadov^^. There are 
partial eclipses of the moon as well as of the sun ; but in 
this case the eclipse is partial because the moon passes 
only through the edge of our shadow (lower orbit in the 
illustration opposite), and so is not wholly darkened. The 
eclipse may be total, however (upper of the three orbits), 
without our satellite passing directly through the center of 
the earth's shadow, because that shadow, where the moon 

TODD'S ASTRON. — 20 



3o6 Eclipses of Sun and Moon 

passes through it, is nearly three times the moon's own 
diameter. A lunar eclipse is always visible to that entire 
hemisphere of our globe turned moonward at the time. 
The total phase lasts nearly two hours, and the whole 
eclipse often exceeds three hours in duration. 

The magnitude of a lunar eclipse is often expressed by digits, that 
is, the number of twelfths of the moon's diameter which are within the 
earth's umbra. The last illustrations show^ different magnitudes of 
lunar eclipse; note the roughness of the terminator. Also the same 
thing may be expressed decimally, an eclipse whose magnitude is i .o 
occurring when the moon enters the dark shadow^ for a moment, and at 
once begins to emerge. 

Diameter of the Earth's Shadow. — As the mean distance of our 
satellite is 239,000 miles, the earth's shadow must extend into space 
beyond the moon a distance equal to the moon's distance subtracted 
from the length of the shadow, or 618,000 miles. The diameter of the 
earth's shadow where the moon traverses it during a lunar eclipse may, 
therefore, be found from the proportion 

857,000 : 7900 : : 618,000 : x. 

This gives 5700 miles, or 2} times the moon's diameter. As our satel- 
lite moves over her own diameter in about an hour, a central eclipse 
may last about four hours, from the time the moon first begins to enter 
shadow to the time of complete emersion from it. 

Lunar Ecliptic Limit. — As our satellite revolves round us in a plane 
inclined to the ecliptic, it is evident that there must be a great variety 



ECLIPSE TOTAL 

AND CENTRAL 



ECLIPSE TOTAL 

BUT ECLIPSE ECLIPSE 

"^OT CENTRAL JUST TOTAL ONLY PARTIAL NO ECLIPSE 




Lunar Ecliptic Limit West of Moon's Ascending Node 

of conditions under which eclipses of the moon take place. Al\ depends 
upon the distance of the center of the earth's shadow from the node of 
the moon's orbit at the time of full moon. The illustration helps to 
make this point plain. It shows a range in magnitude of eclipse, from 
the total and central obscuration (on the left), to the circumstances 
which just fail to produce an eclipse (on the right). The arc of the 



Moon Visible although Eclipsed 307 



ecliptic, about 12° long, included between these two extremes, is called 
the lunar ecliptic limit. It varies in length with our distance from the 
sun ; evidently the farther we are from the sun, the larger will be the 
diameter of the earth's shadow. Also the lunar ecliptic limit varies 
with the moon's distance from us ; because the nearer she is to us, the 
greater the breadth of our shadow which she must traverse. Inside of 
this limit, the moon may come to the full at any distance whatever from 
the nodes. Clearly there is a limit of equal length to the east of the 
node also ; and the entire range along the ecliptic within which a lunar 
eclipse is possible is nearly 25°. As the sun (and consequently the 
earth's shadow) consumes about 26 days in traversing this arc, there is 
an interval of nearly a month at each node, or twice a year, during 
which a lunar eclipse is possible. 

The Moon still Visible although Eclipsed. — Usually the 
moon, although in the middle of the earth's shadow where 
she can receive no direct light from the sun, is neverthe- 
less visible because of a faint, reddish brown illumination. 
Probably this is due to light refracted through the earth's 
atmosphere all around the sunrise and sunset line. At- 
mosphere absorbs nearly all the bluish 
rays, allowing the reddish ones to pass 
quite freely. 

Naturally, if this belt of atmosphere were per- 
fectly clear, the darkened portion of the moon 
might be plainly visible as in the picture of 
the eclipse of 1895 (page 308), while if it were 
nearly filled with cloud, very little light could 
pass through and fall upon the moon ; so that 
when she had reached the middle of the 
shadow, she would totally disappear. Accord- 
ingly there are all variations of the moon's 
visibility when totally eclipsed; in 1848, so 
bright was it that some doubted whether there 
really was an eclipse ; while in 1884 the coppery 
disk of the moon disappeared so completely 
that she could scarcely be seen with the telescope. In September 1895 
the moon, even when near the middle of our shadow, gave light enough 
to enable Barnard to obtain this photograph of the total eclipse, by 
making a long exposure, which accounts for the stars being trails 
instead of mere dots ; for the clockwork was made to follow the mov- 




Total Lunar Eclipse, 3d Sep- 
tember, 1895 (photo- 
graphed by Barnard) 



3o8 



Eclipses of Situ and Moon 



ing moon. Total lunar eclipses are of use to the astronomer in meas- 
uring the variation of heat radiated at different phases of the eclipse. 
Also the occultations of faint stars can be accurately observed, as the 
moon's disk passes over them : and by combining a large number of 
these observations at widely different parts of the earth, the moon's size 
and distance can be more precisely ascertained. Only one total 
eclipse will be visible in America during the remainder of the pres- 
ent century. It occurs 27th December, 1898. Total eclipse begins at 
5.49 P.M., the middle of the eclipse is at 6.34. and the end of total 
eclipse takes place at 7.18 p.m.. Eastern Standard time. So that it 
may be well observed in the eastern part of the United States. 




Lunar Eclipse just before Totality, observed at Amherst College. 10th March, 1895 

Relative Frequency of Solar and Lunar Eclipses. — Draw lines tangent 
to sun and earth, as in next figure. An eclipse of the moon takes place 
whenever our satellite, near J/', passes into the dark shadow cone. On 
the other hand, when near J/, a solar eclipse happens if the moon 
touches any part of the earth's shadow cone extended sunward from E, 
As the breadth of this shadow cone is greater at M than at J/', ob- 
viously the moon must infringe upon it more often at M ; that is, 
eclipses of the sun are more frequent than eclipses of the moon. Cal- 
culation shows that the relative frequency is about as 4 to 3. This 




Eclipse Seasons 309 

means simply with reference to the earth as a whole. If, however, we 

compare the relative frequency of solar and lunar eclipses visible in a 

given country, it will be found that lunar eclipses are much more often 

seen than solar ones. This is 

because some phase of every .^:§|S^^ 

lunar eclipse is visible from 

more than half of our globe, 

while a solar eclipse can be seen 

from only that limited part of ""y^^^^ golar than Lunar Eclipses 

the earth's surface which is 

traversed by the moon's umbra and penumbra. If we consider the 
narrow trail of the umbra alone, a total solar eclipse will be visible from 
a given place only once on the average in 350 years. 

Eclipse Seasons. — It has been shown that eclipses of sun and moon 
can happen only w4ien the sun is near the moon's node. Were these 
points stationary, it is clear that eclipses would always take place near 
the same time every year. But the westward motion of the nodes is 
such that they travel completely round the ecliptic in i8| years. The 
sun, then, does not have to go all the way round the sky in order to 
return to anode; and the interval elapsing between tw^o consecutive 
passages of the same node is only 346I days. This is called the eclipse 
year. On the average, then, eclipses happen nearly three weeks earlier 
in each calendar year. The midyear eclipses of 1898 take place in July, 
of 1899 in June, and of 1900 in May. Each passage of a node marks 
the middle of a period during which the sun is traveling over an arc 
equal to double the ecliptic limit. No eclipse can happen except at 
these times. They are, therefore, called eclipse seasons. As the solar 
ecliptic limit exceeds the lunar, so the season for eclipses of the sun 
exceeds that for lunar eclipses; the average duration of the former is 
37 days, and of the latter 23. 

Recurrence and the Saros. — Ever since the remote age 
of the Chaldeans, B.C. 700, has been known a period called 
the saros, by which the return of eclipses can be roughly 
predicted. The length of the saros is 6585!- days, or 18 
years \\\ days. At the end of this period, the centers of 
sun and moon return very nearly to their relative positions 
at the beginning of the cycle; also certain technical con- 
ditions relating to the moon's orbit and essential to the 
accuracy of the saros are fulfilled. Solar and lunar eclipses 
are alike predictable by it. 



3IO Eclipses of Sun and Moon 

A total eclipse of the sun occurred in Egypt, 17th May, 1882 ; and 
reckoning forward from that date by means of the saros, we can pre- 
dict the eclipses of 28th May, 1900, and 8th June, 191 8. But only in a 
general way ; if the precise circumstances of the eclipse are required, 
and the places where it will be visible, a computation must be made from 
the Ephemeris, or Nautical Almanac. Mark the effect of the one third 
day in the saros : the eclipse at each recurrence falls visible about 120° 
of longitude farther west; in 1882 visible in Egypt, in 1900 on the 
Atlantic Ocean, in 191 8 on the Pacific Ocean. A period of 54 years 
I month I day, or three times the length of the saros, will therefore 
bring a return of an eclipse in very nearly the same longitude, but its 
track will always be displaced several hundred miles in latitude. For 
example, the total eclipse of 8th July, 1842, was observed in central 
Europe ; but its return, 9th August, 1896, fell visible in Norway. About 
70 eclipses usually take place during a saros, of which about 40 are 
eclipses of the sun, and 30, of the moon. 

Life History of an Eclipse. — As to eclipses in their relation to the 
saros, every eclipse may be said to have a life history. Whatever its 
present character, whether partial, total, or annular, it has not always 
been so in the past, nor will its character continue unchanged in the 
indefinite future. New and very small partial eclipses of the sun are 
born at the rate of about four every century ; they grow to maturity as 
total and annular eclipses, and then decline down their life scale as 
merely partial obscurations, becoming smaller and smaller until even 
the moon^s penumbra fails to touch the earth, and the eclipse completely 
disappears. For a lunar eclipse, this long cycle embraces nearly 900 
years, that is, the number of returns according to the saros is almost 
50 ; but solar eclipses, for which the ecliptic limit is larger, will return 
nearly 70 times, and last through a cycle of almost 1200 years. 

Occultations of Stars and Planets by the Moon. — Closely allied to 
eclipses are the phenomena called occultations. When the moon comes 
in between the earth and a star or planet, our satellite is said to occult 
it. There are but two phases, the disappearance and the reappearance ; 
and in the case of stars, these phases take place with startling suddenness. 
Disappearances between new and full, and reappearances between full 
and new, are best to observe, because they take place at the dark edge 
or limb of the moon. When the crescent is slender, a very small tele- 
scope is sufficient to show these interesting phenomena for the brighter 
stars and planets. Occultations of the Pleiades are most interesting and 
important. Many hundreds of occultations of stars are predicted in the 
Nautical Almanac each year. Occultations of the major planets are very 
rare, and none can be well seen in the United States during the remain- 
der of the 19th century. 



CHAPTER XIII 

THE PLANETS 

TETHERED by an overmastering attraction to the 
central and massive orb of the solar system are a 
multitude of bodies classified as planets. Next 
beyond the moon, they are nearest to us of all the heavenly 
spheres, and telescopes have on that account afforded 
astronomers much knowledge concerning them. But be- 
fore presenting this we first consider their motions, and the 
aspects and phases which they from time to time exhibit. 

Motions — Classification — Aspects — Phases 

Apparent Motions of the Planets. — Watch the sky from 
night to night. Nearly all the bright stars, likewise the 
faint ones, appear to be fixed on the revolving celestial 
sphere ; that is, they do not change their positions with 
reference to each other. But at nearly all times, one or 
two bright objects are visible which evidently do not belong 
to the great system of the stars considered as a whole ; 
these shift their positions slowly from week to week, with 
reference to the fixed stars adjacent to them. The most 
ancient astronomers detected these apparent motions, and 
gave to such bodies the general name of planets ; that is, 
wanderers. Their movements among the stars appear to 
be very irregular — sometimes advancing toward the east, 
then slowing down and finally remaining nearly stationary 
for different lengths of time, and again retrograding, that 

3" 



312 



The Planets 



is, moving toward the west. But their advance* motion 
always exceeds their motion westward, so that all, in greater 
or less intervals, journey completely round the heavens. 
None of the brighter ones are ever found outside of the 
zodiac ; in fact. Mercury, which travels nearest to the edge 
of this belt, is always about two moon breadths within it. 
A study of the apparent motions of all the planets reveals 
a great variety of curves. If the motions of the planets 
could be watched from the sun, there would be no such 
complication of figures ; for they exist only because we 
observe from the earth, itself one of the planets, and con- 
tinually in motion as the other sun-bound bodies are. 
Planets' Motions explained by the Epicycle. — The irregu- 
lar motions of the 
planets among the 
stars were ingen- 
iously explained 
by the ancient 
astronomers from 
the time of Hip- 
parchus (b.c. 130) 
onward, by means 
of the epicycle. 
A point which 
moves uniformly 
round the circum- 
ference of a small 
circle whose cen- 

A Planet's Motion in the Epicycle -f-pj. traVCls Uni- 

formly round the periphery of a large one, is said to 
describe an epicycle. 

The figure should make this plain : the center, 6", of the small circle, 
called the epicycle, moves round the center t of the large circle, called 
the deferent '^ and at the end of each 24th part of a revolution, it occu- 




Their Naked-eye Appearance 3 1 3 

pies successively the points i, 2, 3, 4, 5, and so on. But while c is mov- 
ing to I, the point a is traversing an arc of the deferent equal to a^by 
By combination of the two motions, therefore, the point a will traverse 
the heavy curve, reaching the points indicated by b^ ^o, ^,.;, b^, (^.-, when 
c arrives at corresponding points 1,2,3,4,5. In passing from b.^ to 
b^. the planet will turn backw'ard, or seem to describe its retrograde 
arc among the stars. By combining different rates of motion with cir- 
cles of different sizes, it w^as found that all the apparent movements of 
the planets could be almost perfectly explained. This false system, 
advanced by Ptolemy (a.d. 140) in his great work called the Ahnagest^ 
was in vogue until overthrown by Copernicus on the publication of his 
great work De Revohitionibus Corporitni Coelestiuni in 1543. 

Naked-eye Appearance of the Planets. — Mercury can 
often be seen in all latitudes of the United States by 
looking just above the eastern horizon before sunrise 
(in August, September, or October), or just above the 
western horizon after sunset (in February, March, or 
April). In these months the ecliptic stands at a very 
large angle with the horizon, and Mercury will appear as 
a rather bright star in the twilight sky, always twinkling 
violently. Venus, excepting sun and moon the brightest 
object in the sky, is known to everybody. She is always so 
much brighter than any of the other planets that she cannot 
be mistaken — either easterly in the early mornings or 
westerly after sunset, according to her orbital position rela- 
tively to the earth. Usually, when passing near the sun, 
Venus cannot be seen because the sun overpowers her 
rays. During periods of greatest brilliancy, however, 
Venus is not difficult to see with the naked eye when near 
the meridian in a clear blue sky. Mars, when visible, is 
always distinguishable among the stars by a brownish 
red color. Distance from both earth and sun varies so 
greatly that he is sometimes very faint, and again when 
nearest, exceedingly bright. Jupiter comes next to Venus 
in order of planetary brightness. Though much less bright 
than Venus, he is still brighter than any fixed star. Saturn 



314 The Planets 

is difficult to distinguish from a star, because he shines 
with about the order of brightness of a first magnitude 
star. His Hght has a yellowish tinge, and by looking 
closely, absence of twinkling will be noticed. Unless very 
near the horizon, none of the planets except Mercury ever 
twinkle ; and this simple fact helps to distinguish them 
from fixed stars near them. Uranus, just on the limit of 
visibility without the telescope may be seen during spring 
and summer months, if one has a keen eye and knows 
just where to look. Also Vesta, one of the small planets, 
may at favorable times be seen without a telescope. Nep- 
tune is never visible without optical aid. 

Convenient Classifications of the Planets. — Neither appar- 
ent motion, nor naked-eye appearance, however, affords 
any basis for classification of the planets. But distance 
from the sun and size do. In order of distance, succession 
of the eight principal planets with their symbols is as 
follows, proceeding from the sun outward : — 

5 Mercury, 9 Venus, © Earth, ^ Mars, % Jupiter, 
\ Saturn, © Uranus, W Neptune. Of these, Mercury and 
Venus, whose orbits are within the earth's, are classified as 
inferior planets, and the other five from Mars to Neptune, 
as superior planets. In the same category would be in- 
cluded the ring of asteroids, or small planets, between Mars 
and Jupiter. The real motions of the planets round the 
sun are counter-clockwise, or from west toward east. 

Also the planets are often conveniently classified in 
three distinct groups : — 

(I) The inner or terrestrial planets. Mercury, Venus, 
Earth, Mars ; also the unverified intramercurian bodies. 

(II) The asteroids, or small planets, sometimes called 
planetoids, or minor planets. 

(III) The outer or major planets, Jupiter, Saturn, 
Uranus, Neptune. 



Co7ifigtiratio7ts of Inferior Planets 315 

In this classification the zone of asteroids forms a definite line of 
demarcation ; but the basis is chiefly one of size, for all the. terrestrial 
planets are very much smaller than the outer or major planets. Here 
may be included also the zodiacal light, and \\\^ gegenschein, both faint, 
luminous areas of the nightly sky. Probably their light is mere sun- 
light reflected from thin clouds of meteoric matter entitled to considera- 
tion as planetary bodies, because, like the planets, each particle must 
pursue its independent orbit round the sun. All the planetary bodies 
of whatever size, together with their satellites, the sun itself, and mul- 
titudes of comets and meteors, are often called the solar system. 

Configurations of Inferior Planets. — In consequence of 
their motions round the central orb, Mercury and Venus 




Aspects of Inferior and Superior Planets 

regularly come into line with earth and sun, as illustrated 
in above diagram. If the planet is between us and the 
sun, this configuration is called inferior conjunction ; supe- 
rior conjunction, if the planet is beyond that luminary. 
At inferior conjunction, distance from earth is the least 
possible; at superior conjunction, the greatest possible. 
On either side of inferior conjunction the inferior planets 
attain greatest brilliancy ; with Mercury this occurs about 
three weeks, and with Venus about five weeks, preceding 
and following inferior conjunction. For many days near 



3i6 



The Planets 



this time, Venus is visible in the clear blue even at mid- 
day ; but in a dark sky her radiance is almost dazzling, 
and with every new recurrence she deceives the uneducated 
afresh. 

Near her western elongation, in 1887-88, many thought she was the 
^Star of Bethlehem ^ ; and for weeks in the winter and spring of 1897, 
when Venus shone high above the horizon, multitudes in New England 
gave credence to a newspaper story that the brilliant luminary which 
glorified the western sky was an electric light attached to a balloon 
sent up from Syracuse, and hauled down slowly every night about 
9 P.M. Venus will again attain her greatest brilliancy on 

27th October, 1898, elongation east, also on 
5th January, 1899, elongation west; 

but what stories may then be set going is idle to surmise. 

Greatest Elongation of Inferior Planets. — An inferior 

planet is at greatest elongation when its angular distance 

from the sun, as seen 
from the earth, is as great 
as possible. The follow- 
ing illustrations help to 
make these points clear. 
The earth is at the eye 
of the observer, and a 
thin disk about 18 inches 
in diameter, and held 
about one foot from the 
eye, represents the plane 
of the orbits of the in- 
ferior planets. They 
travel round with the 
arrows, passing superior 
conjunction when farthest away from the eye, and there- 
fore of their smallest apparent size. Coming round to 
greatest elongation, they are nearer and larger, and their 
phase is that of the quarter moon. The angle between 




Inferior Planets at Greatest Elongation East 

(after Sunset in Spring) 



Configurations of Superior Planets 317 



Venus and the sun is then 47"^. Mercury at a like phase 
may be as much as 28° distant ; but his orbit is so eccen- 
tric that if he is near perihelion at the same time, he 
may be only 18° from the sun. 

Passing on to inferior conjunction, the phase is a continually 
diminishing crescent, of a gradually increasing diameter, as shown. 
The opposite figure represents 
the apparent position of the or- 
bits (relative to horizon) when 
the greatest eastern elonga- 
tions occur in our springtime. 
The observer is looking west 
at sunset, and the planets at 
elongation shine far above the 
horizon in bright twilight, and 
are best and most conveniently 
seen. When greatest elonga- 
tions west of the sun occur, 
one must look eastward for 
them, before sunrise, as in the 
adjacent illustration (autumn 
inclination to east horizon). 
The ancients early knew that 
Venus in these two relations 
was one and the same planet ; 

but they preserved the poetic distinction of a double name. 
phorus for the morning star, and Hesperus for the evening. 




Inferior Planets at Greatest Eiongation West 
(before Sunrise in Autumn) 



Phos- 



Configurations of Superior Planets. — By virtue of the 
position of superior planets outside our orbit, they may 
recede as far as 180° from the sun. Being then on the 
opposite side of the celestial sphere, they are said to be in 
opposition (page 315). When in the same part of the 
zodiac with the sun, they are in conjunction. Halfway 
between these two configurations a superior planet is in 
quadrature; that is, an elongation of 90° from the sun. 
Opposition, conjunction, and quadrature usually refer to 
the ecliptic, and the angles of separation are arcs of 
celestial longitude, nearly. Sometimes, however, it is 



3i8 



The Planets 



necessary to use conjunction in right ascension,. Inferior 
planets never come in opposition or even quadrature, be- 
cause their greatest elongations are much less than 90"^. 

The Phases of the Planets. — Some of the planets, as 
observed with the telescope, are seen to pass through all 
the phases of the moon. Others are seen at times to 
resemble certain lunar phases ; while still others have no 



(<•••►) 



Phases and Apparent Size of the Planet Mercury 

phase whatever. To the first class belong the inferior 
planets, Mercury and Venus. On approaching inferior 
conjunction, their crescent becomes more and more 
slender, like that of the very old moon when coming to 
new; while from inferior conjunction to superior conjunc- 
tion, they pass through all the lunar phases from new to 
full. As in the case of the moon, the horns of the cres- 
cent are always turned from the sun (toward it, as seen in 
the inverting telescope). When near their greatest elon- 
gation, the phase of these planets is that of the moon at 
quarter. One of Galileo's first discoveries with the first 
astronomical telescope, in 1610, was the phase of Venus. 
None of the superior planets can pass through all the 
phases of the moon, because they never can come be- 
tween us and the sun. 

The degree of phase which they do experience, however, is less in 
proportion as their distance beyond us is greater. Mars, then, has the 
greatest phase. At quadrature the planet is gibbous, about Hke the moon 
three days from full. Mars appears at maximum phase in plate vi, 
page 360. But at opposition, his disk, like that of all other planets, 
appears full. Some of the small planets, too, give evidence of an 
appreciable phase : not that it can be seen directly, for their disks are 



Retrogressive Motion 319 

too small, but by variation in the amount of their light from quadra- 
ture to opposition, as Parkhurst has determined. Jupiter at quadrature 
has a slight, though almost inappreciable, phase Other exterior 
planets — Saturn, Uranus, and Neptune — have practically none. 

Loop of a Superior Planet's Apparent Path Explained. — Refer to the 
figure. The largest ellipse, ABCD^ is the ecliptic. Intermediate ellipse 
is orbit of an exterior planet ; and smallest ellipse is the path of earth 




D 
To explain Formation of Loop in Exterior Planet's Path 

itself. A planet when advancing alw^ays moves in direction GH. The 
sun is at .S". When earth is successively at points marked 1, 2, 3, 4, 5, 
6, 7 on its orbit, the outer planet is at the points marked i, 2, 3, 4, 5, 6, 7 
on the middle ellipse. So that the planet is seen projected upon the 
sky in the directions of the several straight lines. These intersect 
the zone F, G, //, /, of the celestial sphere in the points also marked 
upon it I, 2, 3, 4, 5, 6, 7, and among the stars of the zodiac. Fol- 
lowing them in order of number, it is evident that the planet ad- 
vances from I to 3, retrogrades from 3 to 5, and advances again 
from 5 to 7. Also its backward motion is most rapid from 3 to 4, 
when the planet is near opposition, and its distance from earth is the 
least possible. In general, the nearer the planet to earth, the more 
extensive its loop. 

A Planet when Nearest Retrogrades. — First consider the 
inferior planets of which Venus may be taken as the type. 
Fixed stars are everywhere round the outer ring, represent- 
ing the zodiac (page 320). Within are two large arrows fly- 
ing in the counter-clockwise direction in which the planets 
really move round the sun. Earth's orbit is the outer cir- 
cle in the left-hand figure, and the dotted circle within is 
the orbit of Venus. As Venus moves more swiftly than 



320 



The Planets 



the earth does, evidently the latter may be regarded as 
stationary, and Venus as moving past it at the upper part 
of the orbit, where inferior conjunction takes place. But 
Venus in this position appears to be among the stars far 
beyond the sun, consequently her real motion forward seems 
to be motion backward among the stars, as indicated by 











Superior Planets re-trograde at 
Opposition 



Inferior Planets retrograde at Inferior 

Conjunction 

All Planets retrograde when nearest to, and advance when farthest from, the Earth 

the right-hand arrow at the bottom. Next, consider the 
exterior planet, of which Mars may be taken as the type. 
In the right-hand figure, inner circle is orbit of earth, and 
outer, orbit of Mars ; and as earth moves more swiftly than 
Mars, earth may be regarded as the moving body and Mars 
as stationary. In the upper part of the figure occurs oppo- 
sition, and earth overtakes Mars and moves on past him. 
But Mars is seen among the stars above and beyond it, and 
evidently his apparent motion is westerly, or retrograde, 
in the direction of the small arrow at the top of the figure. 
Thus is reached the conclusion that the appare^it motion 
of all^ the planets^ whethei' iriferior or superior^ is ahvays 
retrograde zvhen they are nearest the earth. 

A Planet when Farthest Advances. — Return to the in- 



Orbits of Inner Planets 321 

ferior planet Venus, and the left-hand figure ; when 
farthest she is in the lower part of her orbit, and her 
apparent position is among the stars still farther below, 
west or to the left of the sun. Advance or eastward mo- 
tion in orbit, then, appears as advance motion forward 
among the stars. Seemingly, Venus is moving toward the 
sun, and will soon overtake and pass behind him. Now the 
exterior planet again. Assuming Mars to remain station- 
ary in the position of the black dot in lower part of orbit, 
earth (in upper part of orbit, w^here distance between the 
two is nearly as great as possible) moves eastward in the 
direction of the arrow through it. As a consequence of 
this motion, then. Mars seems to travel forward on the 
opposite or lower side of the celestial sphere (in the direc- 
tion of a very minute arrow near the bottom of the figure). 
Thus is reached this general conclusion : Tlie apparent 
motion of all the planets^ zvhether inferior or superior, is 
always retrograde zvJien they are Clearest the earthy and 
advance or eastward' when farthest fro7n it. 

Orbits — Ele7ne7its — Pe7'iods — Lazvs of Motio7i 

The Four Inner or Terrestrial Planets. — On next page 
are charted the orbits of the four inner planets, Mercury, 
Venus, earth, and Mars. Observe that while Venus and 
the earth move in paths nearly circular, with the sun very 
near their center, orbits of Mercury and Mars are both 
eccentrically placed. So nearly circular are the orbits of 
all planets that, in diagrams of this character, they are 
indicated accurately enough by perfect circles. Orbits 
having a considerable degree of eccentricity are best repre- 
sented by placing the sun a little at one side of their 
center. 

The double circle outside the planetary orbits represents the ecliptic, 
graduated from o'' eastward, or counter-clockwise, around to 360^ of 
todd's astrox. — 21 



322 



The Planets 



longitude, according to the signs of the zodiac, as indicated ; the vernal 
equinox, or the first point of the sign Aries corresponding to o°. 
Small black dots on each orbit represent positions of the planets at 
intervals of ten days, zero for each planet being at longitude i8o°. All 
the planets travel round the sun eastward, or counter-clockwise, as 




''-'^3'' 



SCALE OF MILLIONS OF MILES 



Orbits and Heliocentric Movenients of the Four Terrestrial Planets 

indicated by arrows. In order to find the distance of any planet from 
earth, or from any other at any time, first find the position of the two 
planets in their respective orbits by counting forward from the dates 
given for each planet on the left-hand side of the chart, at longitude 
1 80°. Then with a pair of dividers the distance of the planets may be 
found from the scale of millions of miles underneath. 

The Four Outer and Major Planets. — Opposite is a chart of the orbits 
of the four outer planets, Jupiter, Saturn, Uranus, and Neptune. Ob- 



True Form of Planetary Orbits 323 

serve that these orbits are all sensibly circular and concentric, except 
that of Uranus, the center of which is slightly displaced from the sun. 
The double outer circle represents the ecliptic, the same as in the 
diagram on the opposite page. The small black dots on the orbits of 
Jupiter and Saturn represent the positions of these planets at intervals 



.. --D, 




* 90"^ 


*4 JOuT^ 


-^ ^ 


^20^;^ 



•..^ 




\.^ 



^^^^_1'"'^40 


^ 


■-^ 


=.>^ 


tji^^^_^ 270'' . . 


^•^ 




■■^^ 


2000 
1 




-■'■'■■-■■■■■V3-----' 

Q 400 800 1200 


1600 




SCALE OF MILLIONS OF 


V1ILES 







Orbits and Heliocentric Movements of the Four Greater Planets 

a year in length ; and similarly, the positions of Uranus and Neptune 
are indicated at lo-year interv^als ; the zero in every case being coinci- 
dent with longitude i8o°. The distance of these planets from each 
other, or from the earth at any time, may be found in the same way as 
described on the opposite page for the inner planets. 

True Form of the Planetary Orbits. — Were it possible 
to transport our observatory and telescope from earth to 



324 The Planets 

each of the planets in turn, and then repeat the meas- 
ures of the sun's diameter with great refinement, just as 
we did from the earth (page 136), we should reach a result 
precisely similar in every case. So the conclusion is, that 
the orbits of all the planets are ellipses, so situated in 



ECLIPTIC PLANE 




Planetary Orbits having Greater Inclinations to the Ecliptic 

s^ ace that the sun occupies one of the foci of each ellipse. 
None of them would lie in the same plane that the earth 
does, but each planet would have an ecliptic of its own, in 
the plane of which its orbit would be situated. 

Inclination and Line of Nodes. — The orbits of all the 
great planets, except Mercury, Venus, and Saturn, are 
inclined to the ecliptic less than 2°. Saturn's inclination 
is 2|-°, that of Venus 3f °, and Mercury's 7°, as in the dia- 
gram. Orbits of the small planets stand at much greater 
angles; six are inclined more than 25"^, and the average 
of the group is about 8°. The two opposite points where 
a planet's orbit cuts the ecliptic are called its nodes. 

Eccentricity of their Orbits. — The eccentricity of Mer- 
cury is \^ of Mars ^^y, of Jupiter, Saturn, and Uranus about 
2^-Q, and of Venus and Neptune very slight. The chief 
effect of the eccentricity is to change a planet's distance 
from the sun, between perihelion and aphelion; and to 
vary the speed of revolution in orbit. At top of next 
page are eccentricities of the planetary orbits, together 
with total variation of distance due to eccentricity. 

Some of the small planets have an eccentricity more than double 
that of Mercury even, so that their perihelion point is near the orbit 
of Mars, while at aphelion they wander well out toward the path of 



Synodic Periods 325 

Eccentricity and Variation of Distance from the Sun 



Eccentricity 


Change of 

Distance due to 

Eccentricity 


Eccentricity 


Change of 

Distance due to 

Eccentricity 


Mercury, 0.2056 
Venus, 0.0068 
Earth, 0.0168 
Mars, 0.0933 


^^ 1 Millions 

'\ of 

^ miles 
26 ^ 


Jupiter, 0.0482 
Saturn, 00561 
Uranus, 0.0464 
Neptune, 0.0090 


47 
90 
166 
49 J 


Millions 

of 

miles 



Jupiter. The average eccentricity of their orbits is excessive, being 
about equal to that of Mercury. The path of Andromache (175) is 
very like the orbit of TempePs comet 11. (page 401). 

Synodic Periods. — Just as with the moon, so each 
planet has two kinds of periods. A planet's sidereal 
period is the time elapsed while it is journeying once com- 
pletely round the sun, setting out from conjunction with 
some fixed star and returning again to it. If during this 
interval the earth remained stationary as related to the 
sun, the times occupied by the planets in traversing the 
round of the ecliptic would be their true sidereal periods. 
But our continual eastward motion, and the apparent 
motion of sun in same direction, makes it necessary to 
take account of a second period of revolution — the 
synodic period, or interval between successive conjunc- 
tions. If a superior planet, the average interval between 
oppositions is also the synodic period. Following are the 

Synodic Periods 



The Terrestrial Planets 



Mercury 116 days 

Venus 584 days 

Mars 780 days 



The Major Planets 



Jupiter 399 days 

Saturn yjZ days 

Uranus 370 days 

Neptune 368 days 



326 



The Planets 



The exceptional length of the synodic periods of Venus 
and Mars is due to the fact that their average daily motion 
is more nearly that of the earth than is the case with any 
of the other planets. 

Sidereal Periods. — As our earth is a moving observa- 
tory, it is impossible for us to determine the sidereal 
periods of the planets directly from observation. But their 
synodic periods may be so found; and from them the true 
or sidereal periods are ascertained by calculation, involving 
only the relation of the earth's (or sun's apparent) motion 
to that of the planet. They are as follows : — 

SmEREAL Periods or Periodic Times 



The Terrestrial Planets 



The Major Planets 



Mercury 88 days 

Venus 225 days 

The Earth 365 \ days 

Mars 687 days 



Jupiter II I years 

Saturn . . . . . . 29} years 

Uranus 84 years 

Neptune 165 years 



Periodic times of the small planets range between three 
and nine years. 

Kepler's Laws. — Kepler, to whom the motions of the 
planets were a mystery, nevertheless had discovered in 1619 
three laws governing their motions. (I) the orbit of every 
planet is elliptical in form, and the sun is situated at one 
of the foci of the ellipse. (II) The motion of the radius 
vector, or line joining the planet to the sun, is such that 
it sweeps over equal areas of the ellipse in equal times. 
(Ill) The squares of the periodic times of the planets 
are proportional to the cubes of their average distances 
from the sun. Kepler was unable to give any physical ex- 
planation of these laws. He merely ascertained that all 
the planets appear to move in accordance with them. 



Distances of Planets from Sun 



327 



Verification of Kepler^s Third Law. — A half hour's calculation suf- 
fices to prove the truth of this law. The results are shown in the last 
column of the following table, where the number in each line was ob- 
tained by dividing the square of the planet's periodic time by the cube 
of its mean distance from the sun. 

Verification of Kepler's Third Law 



Name of 


Periodic Time 


Mean Distance 


[Time]2 


Planet 


(in Days) 


(Earth's Distance = i) 


[Distance]3 


Mercury 


87.97 


0.3871 


133.414 


Venus 


224.70 


0.7233 


133430 


Earth 


365.26 


1 .0000 


I334I5 


Mars 


686.95 


1.5237 


133400 


Ceres 


1681.4I 


2.7673 


133408 


Jupiter 


4332.58 


5.2028 


133.272 


Saturn 


10759.22 


9.5388 


133400 


Uranus 


30688.82 


19-1833 


I334IO 


Neptune 


60181.II 


30.0551 


133403 



The third law of Kepler, often called the 'harmonic law,' is rigorously 
exact, only upon the theory that planets are mere particles, or exceed- 
ingly small masses relatively to the sun. On this account the discrep- 
ancy in the last column is quite large, in the case of Jupiter, because 
his mass is nearly y-J^ ^ that of the sun. 

Mean Distances of the Planets. — Kepler's third law en- 
ables us to calculate a planet's average distance from the 
sun, once its time of revolution is known; for regarding 
the earth's period of revolution as unity (one year), and 
our distance from the sun as unity, it is only necessary to 
square the planet's time of revolution, extract the cube 
root of the result, and we have the planet's mean distance 
from the sun. For example, the periodic time of Uranus 
is 84 years ; its square is 7056 ; the cube root of which is 
19.18. That is, the mean distance of Uranus from the sun 
is 19.18 times our own distance from that central luminary. 



328 



The Planets 



Its distance in miles, then, will be 19. i8 x 93,000,000. In 
like manner may be found the distances of all the other 
planets from the sun ; and they are as follows : — 



Mean Distance from the Sun 



The Terrestrial Planets 


The Major Planets 


Mercury .... 36 
Venus .... b^\ 
The Earth ... 93 
Mars 141 J 


Millions 
. of 
miles 


Jupiter .... 483! ■ 
Saturn .... 886 
Uranus .... 1780 
Neptune . . . 2790 


MiUions 
. of 
miles 



These distances are all represented in true relative pro- 
portion in the figure on page 334. Scattered over a zone 
about 280 millions of miles broad, or | of the distance 
separating Mars from Jupiter, is the ring of small planets, 
or asteroids probably many thousand in number, of which 
nearly 500 have already been discovered. 

The Nearest and the Farthest Planet. — Mars is often said 
to be the nearest of all the planets, because his orbit is so 
eccentric that favorable oppositions, as shown later in the 
chapter, may bring him within 35,000,000 miles of the earth. 
But Venus comes even nearer than that. Her distance 
from the sun subtracted from ours gives 26,000,000 miles 
for the average distance of Venus from the earth at 
inferior conjunctions ; and Venus may approach almost 
2,000,000 miles nearer than this, if conjunction comes in 
December or January, near earth's perihelion. But we 
must not think of Venus as being proportionately easier 
to observe, because so much nearer. It might even be 
said that the nearer Venus comes, the more difficult she 
is to observe, because she is then nearly in line with the 
sun, whose brightness diffused through our atmosphere 



Elements of Planetary Orbits 329 

sets a serious barrier to thorough knowledge of her surface. 
Of the known planets the farthest from the earth is Nep- 
tune. So far away is he that w^e must multiply the least 
distance of Venus more than a hundredfold in order to 
obtain the distance of Neptune from the earth. 

Aberration Time. — Knowing the velocity of light by experiment, 
and knowing the distances of the planets from us, it is easy to calcu- 
late the time consumed by light in traveling from any planet to the 
earth. So distant is Neptune, for example, that light takes about 
\\ hours to reach us from that planet. This quantity is called the 
planet's aberration time, or the equation of light. Its value in seconds 
for any planet is equal to 499 times the planet's distance from the earth 
(expressed in astronomical units). 

Newton's Law of Gravitation. — Sir Isaac Newton about 
1675 simplified the three laws of motion of the planets 
into a single law, hence known as the Newtonian law of 
gravitation. It has two parts of which the first is this : 
that every particle of matter in the universe attracts every 
other particle directly as its mass or quantity of matter ; 
and second, that the amount of this attraction increases 
in proportion as the square of the distance betw^een the 
bodies decreases. That Kepler's three laws are embraced 
in this one simple law of Newton may be shown by a 
mathematical demonstration. With a few trifling excep- 
tions, all the bodies of the solar system move in exact ac- 
cordance with Newton's law, whether planets themselves, 
their satellites, or the comets and meteors. Newton's law 
is often called ^The Law of Universal Gravitation,' be- 
cause it appears to hold good in stellar space as well as 
in the solar system itself. 

Elements of Planetary Orbits. — The mathematical quan- 
tities which determine the motion of a celestial body are 
called the elements of its orbit. They are six in number, 
and they define the size of the orbit, its shape, and its rela- 
tion to the circles and points of the celestial sphere. 



330 The Planets 

{}) a Mean distance, or half the major axis of the ellipse 
in which the planet moves round the sun. 

(2) e Eccentricity, or ratio of distance between center and 

focus of ellipse to the mean distance. 

(3) H Longitude of ascending node, or arc of great circle 

between thi-s node and the vernal equinox. 

(4) / Inclination of plane of orbit to ecliptic. 

(5) TT Longitude of perihelion, or angle between line of 

apsides and the vernal equinox. 

(6) e Longitude of the planet at some definite instant, often 

technically called the epoch. 

Once the exact elements of an orbit are found, the undis- 
turbed motion of the body in that orbit can be predicted, 
and its position calculated for any past or future time. 

Secular Variations of the Elements. — About a century 
ago, two eminent mathematical astronomers of France, 
La Grange and La Place, made the important discovery 
that the action of gravitation among the planets can never 
change the size of their orbits ; that is, the element a^ or 
the mean distance, always remains the same. As for the 
other elements affecting the shape of the orbit and its posi- 
tion in space, they can only oscillate harmlessly between 
certain narrow limits in very long periods of time. These 
slow and minute fluctuations of the- elements are called 
secular variations ; and they may be roughly represented 
by holding a flexible and nearly circular hoop between the 
hands, now and then compressing it slightly, also wobbling 
it a little, and at the same time slowly moving the arms 
one about the other. The oscillatory character of the 
secular variations secures the permanence and stability 
of our solar system, so long as it is not subjected to per- 
turbing or destructive influences from without. One who 
really wishes fully to understand these complicated rela- 



Variatio7t in Apparent Size 331 

tions must undertake an extended course of mathematical 
study — the only master key to complete knowledge of the 
planetary motions. 

Colors — Albedo — Bodes Lazv — Relative Distances 

A Planet when Nearest looks Largest. — In proportion 
as a planet comes nearer to us, its apparent disk fills a 



Variation in Apparent Size of Mars 

larger angle in the telescope. The two planets, then, 
nearest the earth, Venus within our orbit, and Mars with- 
out, must undergo the greatest changes in apparent diame- 
ter, because their great- 
est distance is many 
times their least. Mars, 
at nearest to the earth, 
is 35,000,000 miles away ; 
at farthest, more than 
seven times as distant. 
This seeming variation 

, . , Variation in Apparent Size of Venus 

m size IS shown m above 

figure. The next greatest variation is exhibited by Venus 
(lower figure); at superior conjunctions she seems to be 
only one sixth as large as at inferior conjunction. 

The figure illustrates not only this marked increase of her diameter as 
she comes toward us, but her phases also. Third in order is Mercury, 





332 The Planets 

whose diameters at greatest and least distance are about as i to 3 
(already shown on page 318). And following Mercury is Jupiter, 
whose variations are accurately shown in the adjacent figure. Saturn, 
Uranus, and Neptune, too, show fluctuations of the same character, 
but much less, because of their very great distance from us. From 

conjunction to opposition, the 
apparent breadth of Saturn in- 
creases only about one third ; 
while the similar increase of 
Uranus and Neptune is so 
slight that a micrometer is 
necessary to measure it. 
Apparent Magnitudes and 

Variation in Apparent Size of Jupiter Colors of the Planets. — All 

the planets vary in bright- 
ness, as their distance from the sun and the earth varies. Five of 
them shine with an average brightness exceeding that of a first 
magnitude star. Of these, Venus is by far the brightest, and Jupiter 
next, the others following in the order Mars, Mercury, and Saturn. 
Uranus is about equivalent to a star of the sixth magnitude. Also a 
few of the small planets approach this limit when near opposition. But 
Neptune's vast distance from both sun and earth renders him as faint 
as an eighth magnitude star, so that he is invisible without at least a 
small telescope. The colors of the planets are : 

Mercury, pale ash ; 
Venus, brilHant straw ; 
Mars, reddish ochre ; 
Jupiter, bright silver; 
Saturn, dull yellow ; 
Uranus, pale green ; 
Neptune, the same. 

The entire significance of these colors is not yet known ; but 
apparently they are indicant as to degree and composition of atmos- 
phere enveloping each. 

Albedo of the Planets. — Albedo is a term used to express the capac- 
ity of a surface, like that of a planet, to reflect light. It is a number 
expressing the ratio of the amount of light reflected, from a surface to 
the amount which falls upon it. By observations of a planef s light 
with a photometer, it can be compared with a star or another planet, 
and its albedo found by computation. The moon's surface reflects 
about \ the light falling upon it from the sun. The albedo of Mercury 
is even less, or \ ; but the surface of Venus is highly reflective, its albedo 



Distances and Motions 333 

being I, The albedo of Mars is about \ ; that of Saturn and Neptune, 
about the same as Venus ; while the albedo of Jupiter and Uranus is 
the highest of all the planets, or nearly f . This means that their sur- 
faces reflect about four times as much light as sandstone does. 

The So-called Law of Bode. — Titius discovered a law which approxi- 
mately represents the relative distances of the planets from the sun. It 
is derived in this way. Write this simple series of numbers, in which 
each except the second is double the one before it : 

03 6 12 24 48 96 

Add 4 to each, giving 

47 10 16 28 52 100 

The actual distances of the planets known in the time of Titius 
(1766) are as follows (the earth's distance being represented by 10) : 

3.9 7.2 10 15.2 52.0 95.4 

Although the law is by no means exact, Bode, a distinguished Ger- 
man astronomer, promulgated it. On that account it is always called 
Bode's law. Except historically, this so-called law is now of no 
importance ; for its error, when extended to the outer planets, Uranus 
and Neptune, is even greater than in the case of Saturn. But by direct- 
ing attention to a break in succession of planets between Mars and 
Jupiter, Bode's law led to telescopic search for a supposed missing 
body ; a search speedily rewarded by discovery of the first four small 
planets, (l) Ceres, @ Pallas, (3) Juno, and ® Vesta. 

Relative Distances and Orbital Motions. — Once the distances of the 
planets have been found, measures of their disks with the telescope en- 
able us to calculate their true dimensions. One need not try to improve 
upon Sir John HerschePs illustration of the relative distances, sizes, and 
motions in the solar system. ^ Choose any well-leveled field or bowling 
green. On it place a globe two feet in diameter ; this will represent the 
sun ; Mercury will be represented by a grain of mustard seed, on the 
circumference of a circle 164 feet in diameter for its orbit ; Venus a pea, 
on a circle of 284 feet in diameter ; the earth also a pea, on a circle of 
430 feet ; Mars a rather large pin's head, on a circle of 654 feet ; the 
asteroids, grains of sand, in orbits of from 1000 to 1200 feet; Jupiter 
a moderate-sized orange, in a circle nearly half a mile across ; Saturn a 
small orange, on a circle of four fifths of a mile ; Uranus a full-sized 
cherry or small plum, upon the circumference of a circle more than a 
mile and a half; and Neptune a good-sized plum, on a circle about two 
miles and a half in diameter. ... To imitate the motions of the 



334 



The Planets 



Relative Distances 
and Orbital Motions 
of the Planets 



planets, in the above-mentioned orbits, Mercury 
must describe its own diameter in 41 seconds; 
Venus, in 4 m. 14 s. ; the earth, in 7 m.; Mars, in 
4 m. 48 s. ; Jupiter, in 2 h. 56 m. ; Saturn, in 3 h. 
13. m. ; Uranus, in 2 h. 16 m.; and Neptune, in 
3 h. 30 m.' A farther and helpful idea of relative 
motion of the planets may be obtained from the fig- 
ure, in which Mercury's period round the sun is 
taken as the unit. While he is moving 360-. that is 
in 88 days, the other planets move over the arcs set 
down opposite their distance from the sun. This 
makes very apparent how much the motion of planets 
decreases on proceeding outw^ard from the sun. If 
Neptune moves as an athlete runs. Mercury speeds 
round with the celeritv of a modern locomotive. 



Sizes — Masses — Axial Rotation ■ 
Evohttion 



Tidal 



The Size of the Planets. — Regarding 
the group of small planets as a dividing 
line in the solar system, all planets inside 
that group are, as previously said, rela- 
tively small, and all outside it large. The 
illustration on next page serves to show this 
well, presenting not only the relative sizes 
of the planets, but also the relation of 
their diameters to the sun's. More par- 
ticularly the mean diameters are : — 



Inner 

Terrestrial 

Planets 



Mercury, 
Venus. 

1 Earth. 

I Mars. 



3.000 miles 
7.700 miles 
7,920 miles 
4.200 miles 



Group of small planets : Ceres the largest, 490 
miles in diameter. 



Outer J^P^ter, 
Major ' Saturn, 

-m ^ 1 Lranus, 
Planets i 

^ Neptune, 



87.000 miles 
71.000 miles 
31,700 miles 
34,500 miles 



Their Masses and Densities 



Other small planets whose diam- 
eters have been measured (by Bar- 
nard) are Pallas, 300 miles; Juno, 
120 miles; Vesta, 250 miles. Prob- 
ably none of the others are as 
large as Juno, and the average of 
recent faint discoveries cannot ex- 
ceed 20 miles. 



^Sp5^^p!SS^^«* 



Neptune 

(I satellite) 



Uranus 

(4 satellites)! 



Masses and Densities of Planets. — Best 

by comparison can some idea of the masses 
of the planets be conveyed. Relative Satum 
weights of common things are helpful, and (8 satellites) 
sufficiently precise : Let an ordinary bronze 
cent piece represent the earth. So small are 
Mercury and Mars that we have no coin 
light enough to compare with them ; but 
these two planets, if merged into a single 
one, might be well represented by an old- 
fashioned silver three-cent piece; Venus, 
by a silver dime ; Uranus, a silver dollar, 
half dollar, and quarter together ; Neptune, 
two silver dollars ; Saturn, eleven silver dol- 
lars ; and Jupiter, thirty-seven silver dollars Jupiter 
(rather more than two pounds avoirdupois) . ^^ satellites) 
An inconveniently large sum of silver would 
be required if this comparison were to be 
carried farther, so as to include the sun ; for 
he is nearly 750 times more massive than 
all the planets and their satellites together, 
and, on the same scale of comparison, he 
would somewhat exceed the weight of the ^^^ ^ 
long ton. In striking contrast with this 
vast and weighty globe are the tiny asteroids. Earth 
so light that 300 of them have been esti- (i satellite) 
mated to have a mass of only ^ J^ ^ that of 
our earth. If we derive the densities of 
planets as usually, by dividing mass by vol- 
ume, we find that Mercury is the densest 
of all (one fifth denser than the earth). 
Venus, Earth, and Mars come next, the last 



Snnall 



Planets 



(2 satellites) 



Venus 



Mercury 



^^^^i^^^S^^ 



Relative Sizes of Planets 
(Sun's Diameter on Same Scale 
equals Length of the Cut) 




336 The Planets 

a quarter less dense tKan our globe. Three of the major planets 
have about the same density as the sun himself; that is, only one fourth 
part that of the earth. Saturn's mean density is the least of all, only 
one eighth that of our globe. 

Center of Gravity of the Sun and Jupiter. — Though 
the sun's mass is vastly greater than that of his entire 
retinue of planets put together, he is nevertheless forced 
appreciably out of the position he would otherwise occupy 

by the powerful attrac- 
c^ENTEROF ^ tion of the giant planet 

whose mass is yoVy his 
own. It is easy to calcu- 

Jupiter balancing the Sun j^^^ j^^^^ ^^^j^^ f^^. ^j^^ 

sun and Jupiter revolve round their common center of 
gravity, exactly as if the two vast globes, 5 and J, were 
connected by a rigid rod of steel. But as 5 weighs 1047 
times as much as J, the center of gravity of the system 
is io\y of the distance between the centers of 5 and 
J. Now as Jupiter in perihelion makes this distance 
460,000,000 miles, the center of gravity is displaced from 
wS toward y 440,000 miles. But the radius of the sun is 
433,000 miles; so the center of gravity of the Sun-Jupiter 
system is never less than 7000 miles outside the solar 
orb. And this distance becomes greater as Jupiter recedes 
to his aphelion. 

Axial Rotation of the Planets. — The giant planet turns 
most swiftly on his axis, for the average period of rotation 
of the white belt girdling his equator is only 9 h. ^o\ m. 
But, like the sun, his zones in different latitudes revolve in 
different periods, the average of which is about 9 h. 55|- m. 
The period of revolution of the great red spot averages 
9h. 55 m. 39 s. Saturn, too, exhibits similar discrepancies, 
but the white spots of his equatorial belts gave, in 1893, a 
period of 10 h. 12 m. 53 s. There are indications that the 



Their Librations 337 

axial period of Uranus is about the same; but that of 
Neptune is unknown. Next in order of length is Mars, 
whose day is equal to 24 h. 37 m. 22.7 s., a constant known 
with great precision, because it has been determined by 
observing fixed markings upon the surface, and the whole 
number of revolutions is many thousand. Then comes 
our earth with its day of 23 h. 56 m. 4.09 s. Following, 
though at a long distance, are Mercury and Venus, which 
turn round but once on their axes while going once round 
the sun. The axial period (sidereal) of the former, then 
is 88 days; and of the latter, 225 days, — the longest 
known in the solar system. Her solar day, therefore, is 
infinite in duration, and her year and sidereal day are equal 
in length. This equality of periods, in both Mercury and 
Venus, was undoubtedly effected early in their life history, 
through the agency of friction of strong sun-raised tides 
in their masses, then plastic. 

EUipticity and Axial Inclination of the Planets. — The disks of 
many of the planets do not appear perfectly circular, but exhibit a 
degree of flattening at the poles. This is due to rotation about their 
axes, the centrifugal force producing an equatorial bulge. In the case 
of Jupiter and Saturn, it is so marked as to attract immediate attention 
on examining their disks with the telescope. The polar flattening 
of Saturn's ball is \ (page 367), of Uranus y\, and of Jupiter ^^ 
(page 363), these planets being exceptionally large, and their axial 
rotation relatively swift. Next comes Mars, w^hose polar flattening is 
Y^o, followed by the earth's, ^\-q. The ellipticity of the other planets, 
of the satellites, and of the sun itself, is so small as to escape detection. 
Inclination of planetary equator to plane of orbit round the sun is ex- 
cessive in the case of Uranus ; also probably in Neptune ; has a medium 
value (about 25°) for the earth, Mars, and Saturn ; and is very slight 
for all the other three great planets. 

Librations of the Planets. — There are librations of 
planets, just as there are librations of the moon. But 
the only planetary libration we need to consider is libration 
in longitude. This is due to the fact that, while the planet 

TODD'S ASTRON. — 22 



338 The Planets 

turns with perfect uniformity on its axis, its revolution in 
orbit is swifter near perihelion, and slower near aphelion 
than the average. The amount of a planet's libration in 
longitude, therefore, will depend upon the degree of eccen- 
tricity of its orbit ; and it must be taken into account in 
finding the true period of the planet's day. 

Mercury's libration is the greatest of all. His average daily angle of 
rotation is about 4"^ ; but at perihelion he moves round the sun more 
than 6^, and at aphelion rather less than 3° daily. The effect of libra- 
tion is an apparent oscillation of the disk, alternately to the east and 
west. Starting from perihelion, the angle of revolution in orbit 
gains about 2" each day on the angle of axial turning ; the amount of 
gain constantly diminishing, until nearly three weeks past perihelion. 
Mercury^s libration is then at its maximum, amounting to 23 5° at 
the center of the disk. In the opposite part of his orbit, the disk 
seems to swing as much in the opposite direction, making thus the 
extent of the angle of Mercury's libration equal to 47°. On f of 
his surface, then, the sun never shines. On f it is perpetually 
shining, and on \ there is alternate sunshine and shadow. So, too, 
on Mars, there is an apparent libration of the center of the disk, 
though not so large as Mercury's, because his orbit is less elliptical ; 
and the sun shines on every part of the surface, because the rotation 
and revolution periods of Mars are not equal. Still less are the libra- 
tions of Jupiter and Saturn, their eccentricity of orbit being only 
about half that of Mars. 

Tidal Evolution. — By tidal evolution is meant the dis- 
tinct role play^ed by tides in the progressive development 
of worlds. The term tide is here used, not in its common 
or restricted sense, applying to waters of the ocean, but to 
that periodic elevation of plastic material of a world in its 
early stages, occasioned by gravitation of an exterior mass. 
Newton's law of gravitation first gave a full explanation 
of the rising and falling of ocean tides, but as applied to 
motions of planets, it presupposed that all these bodies 
were rigid. In 1877, George Darwin, in a series of elabo- 
rate mathematical papers, showed the effect of gravitation 
upon these masses in earlier stages of their history, when, 



Transits of Inferior Planets 339 

according to the nebular hypothesis, they were not rigid, 
but composed of yielding material. Ocean tides are raised 
at the gradual, though almost inappreciable, expense of 
earth's energy of rotation. In like manner, earth-raised 
tides in the youthful moon continued to check its axial 
rotation until that effect was completely exhausted, and 
the moon has never since turned on its axis relatively to 
the earth. Evidently this effect of tidal friction has been 
operant in the case of sun-raised tides upon the planets, 
— more powerfully if the planet is nearer the sun ; less 
powerfully if its mass is great ; also less powerfully if its 
materials have early become solidified on account of the 
planet's small size. Combination of these conditions ex- 
plains the present periods of rotation of all the planets : 
Mercury and Venus strongly acted upon by the sun, so 
that they now and for all time turn their constant face 
toward him ; earth, also probably Mars, even yet suffer- 
ing a very slight lengthening of their day; Jupiter and 
Saturn, also probably Uranus and Neptune, still endowed 
with swift axial rotation, because of (i) their massiveness, 
and (2) their vast distance from the center of attraction. 

Transits — Satellites — Atmospheres — Surfaces 

Transits of Inferior Planets. — If either Mercury or 
Venus at inferior conjunction is near the node of the orbit, 
the planet can be seen to pass across the sun like a round 
black spot. This is called a transit. About 13 transits 
of Mercury take place every century, the shortest interval 
being 3 J years, and the longest 13. They can happen 
only in the early part of May and November, because the 
earth is then near the nodes of Mercury's orbit. There 
are about twice as many transits in November as in May, 
because Mercury's least distance from the sun falls near 



340 



The Planets 



the November node. Transits of Venus occur in pairs, 
eight years apart; and the intervals between the midway 
points of the pairs are alternately ii3| and 129^ years. 
June and December are the only possible months for their 
occurrence, and a June pair in one century will be fol- 
lowed by a December pair in the next. Both Mercury 
and Venus at transit, being then nearest the earth, their 
apparent motion is westerly or retrograde. Consequently 
a transit always begins on the east side 
of the sun. Duration of transit varies 
with the part of the disk upon which 
the planet seems to be projected, 
whether north or south of the center 
or directly over the middle. 

Contacts at Ingress and Egress. — Hold the 
book up south. The white arc in the figure 
adjacent will then represent the east limb of 
the sun, upon which the planet enters at in- 
gress, or beginning of transit, as seen in an 
ordinary astronomical telescope. Upper part 
of figure shows the phase called external 
contact. Actual geometric contact cannot of 
course be observed, because it is impossible 
to see the planet until its edge has made a 
slight notch into the sun^s limb. The ob- 
server catches sight of this as soon as possi- 
ble, and records the time as his observation 
of external contact. The planet then moves 
along to the left, until it reaches the phase 
shown at I, a few seconds before internal 
contact. The observer must then watch 
intently the bright horns, which will soon close in rapidly toward each 
other, and finally a narrow filament of light will shoot quickly across 
and join the two horns together. This will be internal contact shown 
at II. After a few seconds the planet will have advanced to III, well 
within the limb of the sun. Then there will be little to observe until 
the planet has crossed the solar disk, and is about to present the 
phases of egress. These will be exactly similar to those at ingress, 
but will take place in reverse order. The atmosphere of Venus (page 




Contacts at Ingress 



Transits of Mercury 



341 



348) complicates observations of these contacts, and they cannot be 
observed within two or three seconds of time. 

Past and Future Transits of Mercury. — Gassendi made the first 
observation of a transit of Mercury in 1631. The annexed engraving 
shows the paths of Mercury during all transits from 1868 to 1924. 



\907 



D\R£CT 



^O. OF TRANSIT ^ 



,vembeR 



^'f^ECT, 



ION OP ^ 



"i894 



J924 



THE ECLIPTIC 



188\ 



/h^ 



\9ii_ 



Paths of Transits of Mercury at Ascending and Descending Nodes 

The circle represents the disk of the sun ; near the top is north, and 
below the right side west. The broken line is part of the ecliptic. Con- 
sider first the November transits. Their dates are : 5th November, 1868 ; 
7th November, 1881 ; loth November, 1894 ; 12th November, 1907 ; 6th 
November, 1914. Mercury is then near ascending node; and the 
paths of these transits are drawn at an ascending angle of about 7^ to 
the ecliptic, this being the inclination of Mercury's orbit to that plane. 
Dots on these paths show positions at half-hour intervals. Observe 
how far apart they are. This is because Mercury is near perihelion, 
where swifter motion carries him quickly across the sun. Next, con- 
sider the May transits. They are only three in number in the same 
interval, and their dates are: 6th May, 1878; 9th May, 1891 ; 7th 



342 



The Planets 



May, 1924. They occur near Mercury's descending node, as shown, 
that of 1924 being nearly central because Mercury happens to come to 
inferior conjunction with the earth, at very nearly the time of reaching 
its node. The half-hour dots are nearer together than in November 
transits, because Mercury is near aphelion, and consequently his motion 
is as slow as possible. The greatest length of a transit of Mercury 
is 7 h. 50 m., and the transit of 1924 approaches near this limit. 

Past and Future Transits of Venus. — Jeremiah Horrox made the 
first observation of a transit of Venus in 1639. Nearly every century 
witnesses a pair of these transits. Below are four disks representing 




s s 

Paths of Transits of Venus at Ascending and Descending^ Nodes 



the sun ; and upon them are indicated apparent paths of Venus, for 
all transits occurring in the 17th to the 21st centuries inclusive. In each 
case the top of the disk is north, and the right-hand side west. The 
dots show the position of the planet at intervals of fifteen minutes. 
Pairs of transits take place at average intervals of \\ centuries ; so there 
will be no transit of Venus in the 20th century. 

Dates of Transits of Venus 



At the Ascending Node 


At the Descending Node 


1631, December 7 
1639, December 4 
1874, December 9 
1882, December 6 


1761, June 5 
1769, June 3 
2004, June 8 
2012, June 6 



As is evident from the figure, a pair of transits at ascending node 
(163 1 and 1639) is followed by a pair at descending node (1761 and 
1769), and so on alternately. Southern transits at ascending node 
(1639 and 1882) are followed by southern transits at descending node 



Their Satellites 343 

(1761 and 2004) ; and a northern transit at descending node (1769) is 
followed by a northern transit at ascending node. Rows of black dots 
in contact with each other indicate the chord of the sun's disk traversed 
at each transit, as seen from the center of the earth. The greatest 
possible length of a transit of Venus is 7 h. 58 m., and the shortest 
one ever observed was that of 1874. Transits of Venus are phe- 
nomena of great interest to astronomers, because proximity of the 
planet produces a large effect of parallax. By measuring it, her dis- 
tance from the earth is found. This tells us the scale on which the 
solar system is built, including therefore the length of the unit in 
astronomical measures, the sun's mean distance from the earth. The 
transits of 1769 and 1882 were visible in the United States. Those of 
1874 and 1882 were extensively observed by costly expeditions under 
the auspices of the principal governments. 

Satellites of the Planets 

Satellites of the Terrestrial Planets. — The solar system 
has this curious and interesting feature, that most of its 
chief planets are accompanied by moons or satelHtes. 
Twenty-one are now known. No satellite has yet been 
discovered belonging to either of the inferior planets. 
There have, however, been many spurious observations of 
a supposed satellite of Venus. Our earth has but one. 
Mars has two satellites, discovered by Hall in 1877. They 
are about seven miles in diameter, and can be seen only by 
large telescopes under favorable conditions. Phobos, the 
inner moon of Mars, is less than 4000 miles from the planet's 
surface, and travels round in 7 h. 39 m., a period less than 
one third that of Mars' rotation. To an observer on the 
planet, Phobos must, therefore, seem to rise in the west 
and set in the east. Its horizontal parallax is enormous, 
being 2i|^°. The outer moon, Deimos, is rather more than 
12,000 miles from the surface of Mars, and its periodic 
time is 30 h. 18 m. As the planet's day is 24 h. 37 m., 
Deimos must consume, allowing for parallax, about 2\ 
days in leisurely circuiting the Arean sky from horizon 
to horizon. 



344 



The Planets 



Satellites of the Major Planets. — Jupiter, has five moons, 
the fifth or innermost discovered only in 1892 by Barnard. 
The four large ones were discovered by Galileo in 1610 
with the first telescope ever used astronomically. The 
orbits of Jupiter's moons lying nearly in the ecliptic are 
always seen edgewise, or very nearly, so that the satellites 
in traveling round the primary seem merely to oscillate 
forth and back, just as the pedals of a distant bicycle, 
moving toward or from us, seem simply to rise and fall. 
Saturn is very rich in attendants, having not only the 
wonderful rings (quite different from everything else in 
the solar system, and undoubtedly made up of an infinity 
of small individual bodies or satellites, too small ever to 
be separately seen), but in addition eight distinct satellites 
are known. Uranus has four moons, and far-away Nep- 
tune has one attendant body. The paths of all these 
satellites are nearly circular, except those of our moon and 
Hyperion. 

Periods, Transits, Occultations, and Eclipses. — Following 
are the principal data of the satellites of Jupiter : — 

The Satellites of Jupiter 



Num- 
ber 


Diameter 


Distance from 
Jupiter 


Sidereal Period of 
Revolution 


Mass in 
Terms of 
Jupiter 


V 


100 miles 


II 2,000 miles 





d. II h. 57 m. 22.7 s. 


? 


I 


2500 


261,000 


I 


18 27 33.5 


60J00 


II 


2100 


415,000 


3 


13 13 42.1 


47^00 


III 


3600 


664,000 


7 


3 42 334 


11000 


IV 


3000 


1,167.000 


16 


16 32 II. 2 


25^00 



So near Jupiter is the fifth satellite that his disk, as seen from the 
surface of the satellite, would stretch more than half way from horizon 
to zenith. Referring to conditions which produce eclipses of sun and 



Light Reqtiires Time to Travel 



345 



moon, illustrated on page 293, and remembering that the orbits of 

Jupiter's satellites nearly coincide with the 

plane of his path, it is clear that eclipses of 

the sun and of Jupiter's moons must occur 

every time a satellite goes round the planet. 

So there are nearly 9000 eclipses of the 

sun and moons annually, from some point 

or other of Jupiter's disk. The iv satellite 

alone escapes eclipse — about half the time. 

When the dark shadow of a satellite is 

seen to cross the disk, it is called a transit 

of the shadow ; and the projection of the 

satellite itself on the disk is called a transit of 

the satellite. In the opposite part of their 

orbits, a satellite's passing behind the disk is called an occupation ; 

and its dropping into the planet's shadow is called an eclipse. Eclipses 

vary from just a few minutes to nearly five hours in length. Eclipses, 

occultations, and transits are predicted many years in advance in the 

Ephemeris^ and are very interesting to observe, even with small tele- 
scopes. An opera glass will show at a glance the moons which are not 
in transit, occultation, or eclipse. Sometimes all four dis- 
appear for a time, though not again in the 19th century. 




Jupiter (Shadow of Satellite in 
Transit) 




Light requires Time to travel. — In 1675, 
Roemer first suspected this, because he found 
that when Jupiter was in opposition, eclipses 
of his satellites took place several minutes 
earlier than the average, and when in conjunc- 
tion, the same amount later. The figure shows 
why; for when Jupiter is in conjunction, sun- 
light reflected from a satellite must journey an 
entire diameter of the earth's orbit farther 
than at opposition. Eclipses of all four moons 
exhibited the same discrepancy. So the con- 
clusion was manifest, that light requires a definite time to 
travel; and we now know, from elaborate calculations, 
that light from these moons travels across the earth's 
orbit in 998 seconds. Half this number, or 499, is the 
constant factor in 'the equation of light.' Its careful 




EARTH 

(jupiter in 
conjun.cti.on) 



346 



The Planets 



determination is a matter of great importance, and eclipses 
of Jupiter's satellites are now recorded with high accuracy 
by the photometer and by means of photography. 

Physical Peculiarities of Jupiter's Satellites. — The first satellite is 

not a sphere, but a prolate 
ellipsoid, its longer axis being 
directed toward the center of 
Jupiter — a remarkable peculi- 
arity discovered by W. H. Pick- 
ering and verified by Doug- 
lass. Markings, very faint in 
character, have been seen upon 
all the satelhtes. By means of 
these their periods of axial rev- 





IX 


\ 




r> 


-A 


:>.\ 


\ x^k^^ 


\ 


V 


IT 


\/\ 


^L 













Markings on Jupiter's 3d Satellite (Douglass) 



olution are found. Fading out at the edge may be indication that in 
possesses an atmosphere. Satellites ni and iv, also probably i and ii, 
turn round once on their axes while going once round Jupiter, a rela- 
tion like that of our moon to the earth. Douglass, from observations 
of very narrow belts on in in 1897, makes its period of rotation 7 d. 5 h. 
Also he has published the adjoining sketch-map of the satellite's sur- 
face. Near the poles of in and iv white spots have been seen by sev- 
eral observers. 

Satellites of Saturn. — Following are the principal data 
of the satellites of Saturn : — 



The Satellites of Saturn 



Num- 
ber 


Name of 
Satellite 


I 


Mimas 


II 


Enceladus 


III 


Tethys 


IV 


Dione 


V 


Rhea 


VI 


Titan 


VII 


Hyperion 


VIII 


lapetus 



Name of 
Discoverer 



W. Herschel 
W. Herschel 
J. D. Cassini 
J. D. Cassini 
J. D. Cassini 
C. Huygens 
W. C. Bond 
J. D. Cassini 



Date of 
Discovery 



17 Sept. 1789 
28 Aug. 1789 
21 Mar. 1684 
21 Mar. 1684 
23 Dec. 1672 
25 Mar. 1655 
16 Sept. 1848 
25 Oct. 167 1 





Distance 


Diameter 


from 




Saturn 


miles 


miles 


750 


117,000 


800 


157,000 


1 100 


186,000 


1200 


238,000 


1590 


332,000 


3500 


771,000 


500 


934,000 


2000 


2,225,000 



Sidereal 
Period of 

Revolution 



d. h. m. s. 

22 37 5.7 

1 8 53 6.9 

1 21 18 25.6 

2 17 41 9.3 
4 12 25 II. 6 

15 22 41 23.2 
21 6 39 27.0 
79 7 54 17.1 



Satellite of Neptune 



347 



The orbits of the five inner satellites are circular. The 
satellites first discovered are easiest to see, the largest, 
Titan, being nearly always visible even with very small 
instruments. Its mass according to Stone is -^^-^-^ that of 
Saturn. Eclipses and transits of some of the satellites 
have occasionally been observed with large telescopes. 

Satellites of Uranus. — Following are the principal data 
of the satellites of Uranus : — 



The Satellites of Uranus 



Number 


Name of 
Satellite 


Distance from 
Uranus 


Sidereal Period of Revolution 


I 

II 

III 

IV 


Ariel 
Umbriel 
Titania 
Oberon 


120,000 miles 
167,000 
273,000 
365,000 


2d. 

4 
8 

13 


12 h. 29 m. 21. 1 s. 
3 27 37.2 
16 56 29.5 
II 7 64 



The two inner satellites are about 500 miles in diameter, 
and the outer ones are nearly twice as large. For the next 
fifteen years, while the earth is near a line perpendicular 
to their orbits, the satellites may always be seen whenever 
Uranus is visible. Only great telescopes, however, will 
show them. The satellites of Uranus revolve in planes 
nearly at right angles to the planet's orbit, and their 
motion is retrograde, or from east to west. Ariel and 
Umbriel were discovered by Lassell in 185 1 ; Titania and 
Oberon, by Sir William Herschel in 1787. 

Satellite of Neptune. — Its distance from Neptune is 
224,000 miles, the period of revolution 5 d. 21 h. 3 m., with 
motion retrograde. It was discovered by Lassell in 1846, 
only a few weeks after the planet itself was found. Prob- 
ably Neptune's satellite is about the size of our own moon. 



348 The Planets 

Atmospheres of the Planets 

Atmosphere of Mercury. — Without much doubt, the 
atmosphere of Mercury is inappreciable. His color by 
day, when best observable, resembles that of the pale moon 
under like conditions. If there is no air, then quite cer- 
tainly no water ; as evaporation would continue to supply 
a slight atmosphere as long as it lasted. The .improba- 
bility of an atmosphere surrounding this planet is con- 
firmed by the argument from the kinetic theory of gases, 
already stated (page 244); for Mercury's mass is too slight 
to retain an envelope of aqueous vapor. 

Atmosphere of Venus. — Observations of Venus when 
very near her inferior conjunction prove the existence of 

an atmosphere which is thought 
to be more dense than ours. The 
illustration shows part of the evi- 
dence : Venus is just entering 
upon the sun's disk during the 
transit of 1882, and sunlight shin- 
ing through the planet's atmos- 
phere illuminates it in a nearly 
complete ring surrounding Venus, 
which appears dark because her 
sunward side is turned away from 
us. Also an aureole surrounds 
the dark disk when in transit ; and 

Venus entering the Disk of the Sun i • i tt 

ini882(Langiey) ^n scvcral occasious whcn Vcuus 

has passed close above or below 
the sun at inferior conjunction, just escaping a transit, 
the horns of the atmospheric ring have been observed 
almost to meet, forming a nearly complete ring. This 
crescent would be little more than a complete semicircle, 
if there were no atmosphere. 




Atmospheres of the Planets 349 

Atmosphere of Mars. — Doubtless a thin atmosphere en- 
velops this planet, although neither so extensive nor so 
dense as our own. While usually cloudless, occasional and 
temporary veilings of some of the best known regions of 
the planet have been seen. Many careful investigators, 
using the spectroscope, have found absorption lines in the 
spectrum of Mars thought to be due to neither solar nor 
terrestrial atmosphere, indicating water vapor in a gas- 
eous envelope. Also regular shrinking and subsequent 
enlarging of the polar caps are excellent evidence that the 
ruddy planet is surrounded by a medium acting as an 
agent in the formation and deposition of snow. Chang- 
ing intensity of the light, with a change of the planet's 
phase also indicates the presence of an atmosphere. 
Another important piece of evidence is the discovery of a 
twilight arc of about 12°, causing a regular increase of the 
planet's apparent diameter through the equator, as phase 
increases. Quite certainly density of the atmosphere of 
Mars cannot exceed one half that of our own, and prob- 
ably it is very much less. Referring again to the kinetic 
theory of gases, and calculating the critical velocity for 
Mars, we find it to be rather more than three miles per 
second. Free hydrogen, then, could not be present in his 
atmosphere, but other gases might. Campbell and Keeler 
have found the spectrum of Mars practically identical with 
that of the moon, indicating probably that the spectro- 
scopic method is inconclusive. 

Atmosphere of Jupiter and Saturn. — The indications of a 
dense and very extended atmosphere encircling Jupiter 
are unmistakable : — ceaseless changes in markings called 
belts and spots; varying length of the planet's day in dif- 
ferent regions of latitude; absorption shadings in the in- 
ferior portion of Jupiter's spectrum; and withal his giant 
mass potent to retain captive all gaseous materials origi- 



350 The Planets 

nally belonging to him. Probably in point of both depth 
and chemical constitution, the atmosphere of Jupiter is 
widely diverse from our own ; in fact, it is not unlikely 
that this great planet may still be in a gaseous condi- 
tion throughout. At least the depth of atmosphere must 
be reckoned in thousands of miles. Dark bands in the 
red may be due to some substance in the planet's at- 
mosphere not in our own, and possibly metallic. In 
nearly every respect the atmosphere of the ball of Saturn 
resembles that of Jupiter, but the ring gives every appear- 
ance of being without atmosphere. Saturn's spectrum, too, 
is quite the same as Jupiter's, and its intenser absorption 
bands indicate a little more plainly the presence of gaseous 
elements as yet unrecognized on the earth and in the 
sun. Another indication of atmosphere, common to both 
these planets, is the shading out or absorption of all mark- 
ings at the limb or edge of their disks. 

Atmosphere of Uranus and Neptune. — So remote are 
these planets, and so small their apparent disks, that practi- 
cally nothing has yet been ascertained concerning their 
atmospheres except by the spectroscope. Uranus is bright 
enough so that its spectrum shows lo broad diffused 
bands, between C and F, indicating strong absorption by a 
dense atmosphere very different from that of the earth, 
as Keeler has shown. The position of these lines in the 
red is sufficient to account for the sea-green tint of the 
planet. Neptune's color is almost the same ; and its spec- 
trum, if not so faint, would probably show similar absorp- 
tion bands. 

Surfaces of the Planets 

Zodiacal Light. — Interior to the orbit of Mercury, but 
possibly stretching out beyond the path of the earth, is 
a widely diffused disk of interplanetary particles moving 



The Gegenschein 



351 



round the sun, mildly reflecting its rays to us, and called 
the zodiacal li^ht. 



The illustration shows it well — a faintly luminous and ill-defined 
triangular area, expanding downward along the ecliptic toward the 
western horizon, short- 
ly after twihght on 
clear, moonless nights 
from January to April. 
Its central region is 
brightest and slightly 
yellowish. It has suf- 
fered no change for 
more than two centu- 
ries. Its spectrum is 
short and continuous, 
without bright lines, 
though possibly a few 
faint dark ones are 
present. In tropic 
latitudes, where the 
ecliptic always stands 
high above the hori- 
zon, the zodiacal light 
can be well seen in 
clear skies the year 
round. In our middle 
latitudes it cannot be 
seen early in autumn 
evenings, because of 
the slight inclination 
of the ecliptic to the 
horizon, as the next 
figure shows : that part 

of the zodiacal light near a and above the horizon, ////, is lost in 
low-lying mist and haze. • In autumn it must be looked for in the east 
just before dawn, leaning tow^ard the right in our latitudes. 

The Gegenschein. — This is a name of German origin, given to a 
zodiacal counterglow^ discovered by Brorsen in 1854 — an exceedingly 
faint and evenly diffused nebulous hght, nearly opposite the sun, some- 
times slightly south and again somewhat north of the ecHptic. A 
bright star or planet near by is sufficient to overmaster its light ; even 
proximity to the Milky Way obliterates it. Sometimes the gegenschein 




The Zodiacal Light in Tropic Latitudes 



352 



The Planets 



is circular, at others elliptic ; and its diameter varies between 3° and 13'', 
according to Barnard and Douglass. It is best seen in September and 

October/ in Sagittarius 
and Pisces. No satisfac- 
tory theory as to its cause 
exists. Very likely the 
gegenschein is due to 
clouds of small inter- 
planetary bodies, though 
possibly it may be caused 
by abnormal refraction in 
our atmosphere. 




Why Zodiacal Light is Invisible in our Fall Evenings 



Surface of Mercury. — Mercury is so small a planet and 
so distant from the earth that the disk is disappointing. 
In the northern hemi- 
sphere he is best seen 
near greatest elongation 
east in spring, and great- 
est elongation west in 
autumn ; because he is 
then in the northernmost 
part of the zodiac, wliere 
meridian altitude is as 
great as possible. Mark- 
ings on the surface of 
Mercury are described by 
Lowell as less difficult 
than those on Venus ; 

without color, and lines rather than patches ; and the fact 
that they do not change from hour to hour, nor per- 
ceptibly from day to day, shows that the planet's periods 
of rotation and revolution are the same. Above are nine 
drawings of the planet in October, 1896; also on the next 
page Lowell's chart of all that portion of the surface of 
Mercury ever visible, amounting to five eighths of the 
entire spherical superficies. The surface is probably rough, 




Typical Drawings of Mercury, 1896 (Lowell) 



Surface of Veiitcs 



353 



because, like the moon, the amount of Hght reflected 
from a unit of surface increases from crescent phase 
to full. 

Illuminated Hemisphere of Venus. — The unillumined 
half of Venus appears to be forever sealed from investiga- 
tion by our eyes ; but 
that part of the sunward 
hemisphere turned to- 
ward us has been repeat- 
edly drawn during the 
last 250 years. Only dull, 
indefinite markings, or 
spots covering large areas 
have, however, been seen 
until recently. The illus- 
tration below shows the 
general nature of mark- 
ings drawn by the earlier observers. Frequently the ter- 
minator was irregularly curved, indicating mountains of great 




Chart of All the Visible Surface of Mercury 

(.Lowell) 




Venus as drawn by Mascari in 1892 

height; and polar caps were depicted. According to recent 
observations of Lowell, however, the disk of Venus is color- 
less, and resembles 'simply a design in black and white 
over which is drawn a brilliant straw-colored veil.' This 

TODD'S ASTRON. — 23 



354 



The Planets 



veil is doubtless the planet's atmosphere. No polar caps 
were seen. 

Markings on the disk, seen and drawn independently by Lowell and 
his assistants, Douglass, See, and others, are broad belts, not spots. 

Three specimen drawings are 
adjacent. The markings are 
mostly great circles on the 
planet's surface, and many 
of them radiate from a sin- 
gle center, as the accom- 
panying chart shows. They 
partake of the general bril- 
liance of the disk, and their 
lack of contrast renders them difficult objects, except to observers 
trained in visualizing faint planetary detail. Three slight protuber- 
ances, probably mountains, were detected on the terminator. This 
interesting work of the LoAvell Observatory, located at Flagstaff, 
Arizona, was done in the latter months of 1896. The fine atmos- 
pheric conditions of that region, and the critical manner in which 
the observations were made. 



• • 



Venus as drawn by Lowell in 1896 



lend significance to the fore- 
going results, although they 
are not as yet fully confirmed 
by observers in other parts 
of the world. Taken in con- 
nection with the practical cer- 
tainty of an atmosphere, the 
constant aspect of one hemi- 
sphere perpetually toward the 
sun is very significant ; prob- 
ably atmospheric currents 
would gradually remove all 
water and nearly all moisture 
from the sunward hemi- 
sphere, and deposit it as ice 
on the dark side of the 
planet. This affords a likely 

explanation of the so-called phosphorescence of the dark hemi- 
sphere ; for a faint light diffused over the unilluminated portion of 
the disk has repeatedly been seen by many good observers. 

Surface of Mars in General. — Huygens, in 1659, made 
the first sketch of Mars to show definite markings; and in 




Chart of Visible Hemisphere of Venus (Lowell) 



Surface of Mars 



355 



1840, Beer and Maedler drew the first chart of the planet. 
The two hemispheres exhibit a marked difference in bright- 
ness, the northern being much brighter. Probably it is 
land, while the southern is mainly water; but in general 
there is no analogy with the present scattering of land 
and water on the earth. Four to eleven is the proportion 
here ; but on Mars land somewhat 
predominates. Probably the waters 
have for the most part sHght depth. 
Extensive regions which change from 
yellow, like continents, to dark brown, 
are thought to be marshes, varying 
depth of water causing the diversity 
of color. Mars appears to be so far 
advanced in his life history that areas 
of permanent water are very limited. 
The border of the disk is brighter 
than the interior, and changes in ap- 
parent brightness of certain regions 
are well established. In consider- 
able part these depend upon the an- 
gle of vision as modified by axial 
turning of the planet. Photographs 
of Mars have been taken, but they 
show only salient features of the disk. 
Major, a well-known region (see fifth figure on page 358) 
appear to be vegetation rather than water. Smoothness 
of the terminator, along which a few projections and 
flattenings have been observed, indicates clearly that the 
Martian surface is relatively flat, as compared with the 
present rugged exterior of earth and moon. 

Orbits of Earth and Mars. — Inner circle in next illustration rep- 
resents orbit of earth, and outer one orbit of Mars eccentrically placed 
in true proportion. Around inner circle are indicated positions of earth 




Mars in 1877 iGreen) 



Markings of Syrtis 



356 



The Planets 



in different months, and around outer circle are shown the points occu- 
pied by Mars at opposition time in the several years indicated. The 
most favorable opposition of Mars, or when that planet is at the mini- 
mum distance of 35,000,000 miles from the earth, can take place only 
in August and September, as indicated on right-hand side of diagram. 




Orbits of Mars and Earth, showings Least and Greatest Distances at Opposition 

Similarly on left-hand side the least favorable oppositions occur in those 
years when the opposition time falls in February and March. Exact 
positions of Mars at recent favorable oppositions are shown at 1877 
and 1892. But at opposition, October, 1894, although the planet was 
then much farther from earth, still he culminated higher than in 1892 ; 
because the sun crosses the meridian lower in October than in August. 
Higher northern declination enabled the planet to be observed to 
greater advantage in 1894 than in 1892, because nearly all the observa- 
tories of the world are located in its northern hemisphere. Subsequent 



Polar Caps of Mars 



357 



opposition distances of Mars are all unfav- 
orably great until 1907 ; or better still, 1909, 
which will occur in September, in nearly the 
same longitude as did that of 1877. 

Polar Caps of Mars. — These were 
discovered by Cassini in 1666. 
Rather more than a century later, 
Sir William Herschel first made out 
their variation in size with progress 
of the seasons on Mars, which are 
in general similar to ours, although 
longer, because the Arean year is 
longer. Near the end of Martian 
winter the polar caps are largest, 
and they gradually shrink in size 
till the end of summer. 



S.^.f:^fS0J^ 



This remarkable diminution of the south 
polar cap has been repeatedly observed since 
HerschePs time, and the illustrations show 
its progress during the Martian spring and 
summer of 1894. Without much doubt, 
this shrinking of the polar cap is due 
to melting of snow and ice. The north 
polar cap exhibits a like succession of phe- 
nomena, though much more difficult to 
observe, because the direction of the planet's 
axis in space is such that when this pole is 
turned toward us. Mars at opposition is 
nearly twice as far away as when the 
south pole is toward us. The north polar 
cap covers the planet's pole of rotation 
almost exactly ; but the center of the 
south is now displaced about 200 miles 
from the true pole, and this distance varies 
irregularly from time to time. At the 
beginning of the summer season of 1892, 
the south polar cap was 1200 miles in diam- 
eter ; gradually a long, dark line appeared 
near the middle, and eventually cut the cap 
in two ; the edge became notched ; dark 



'*;^-" 



Shrinkage and Disappearance 
of South Polar Cap in 1894 
(Barnard in Popular Astronomy) 




(I) Top of Fork on left is Fastigium Aryn. 
Dark Horn nearly central is Margaritifer Sinus 



(2) Sol is Lacus is nearly central. 
Double Nectar runs to the left from it 




(3) Seven Canals diverge from Sinus Tita- 
num, Eumenides-Orcusthreads NineOases 



(4) The Rectangle is Trivium Charontis. 
Dark Mare Cimmerium is central 




(5) Largest Roundish Area is Hellas. 
Below Hellas is the pointed Syrtis Major 



(6) AmiOng Double Canals are Euphrates 
(nearly vertical), and Asopus perpendicularto it 



Mars according to Schiaparelli and Loweil (1877-1894) 

358 



Canals a)id Oases of Mars 359 

spots grew in its central regions, and isolated patches were seen to 
separate from the principal mass, and later dissolve and disappear. 
The phenomenon w^as similar in 1894, as Barnard's 12 pictures of 
the cap show (page 357). In three months the cap's diameter had 
shrunk to 170 miles, and in eight months it had vanished entirely. 

Canals and Oases of Mars. — This diminution of the polar 
cap seems to afford a key to the physiographic situa- 
tion on Mars ; for, coincidently with its shrinking, a strange 
system of markings begins to develop, traversing continen- 
tal areas in all directions, and forming a network of dark- 
ish narrow lines. 

Six engravings opposite exhibit the planet's surface in all longitudes, 
and show the canals much intensified. All appear on the flat disk as 
either straight or uniformly curving lines ; and if transferred to the sur- 
face of a globe, they are found to traverse it on arcs of great circles. 
Many canals connect with projections of bluish-green regions, which 
may be actual gulfs and bays. At numerous intersections with other 
canals are oval or circular spots, called oases, many of them appearing 
like hubs from which canals radiate as spokes. Their average diameter is 
about 130 miles. For example, seven canals converge to Lacus Phoenicis. 
The most signal marking of this character is in Arean latitude about 30° 
south (shown above middle of the second disk opposite). Though 
often called the ' oculus,' or eye of Mars, it is now generally known as 
Soils Lacus, or Lake of the Sun. Its breadth is 300 miles, and its length 
540 miles. Through Solis Lacus run narrow double canals, whose 
length is much less than the average. In general the canals average 
about 1200 miles ; but the longest one is Eumenides-Orcus, whose com- 
bined length is 3500 miles, or nearly equal to the entire diameter of 
the planet. Length enhances their visibility, for the average width is 
only about 30 miles. Canals were first discovered by Schiaparelli in 
1877. They are bluish-green in color, and have been repeatedly ob- 
served by their discoverer in Italy ; Lowell, in Arizona ; Perrotin, in 
France; W. H. Pickering, in South America; astronomers of the Lick 
Observatory ; Wilson, in Minnesota ; and Williams, in England. About 
200 have been seen in all ; so that their reality is now generally con- 
ceded. But a steady atmosphere is requisite to reveal them. 

Doubling of the Canals and Oases. — Lowell, one of the few ob- 
servers who have yet seen the doubling of the canals, thus describes 
this marvelous phenomenon : — 

^ Upon a part of the disk where up to that time a single canal has 
been visible, of a sudden, some night, in place of the single canals, are 



360 The Planets 

perceived twin canals, — as like, indeed, as twins, if not more so, run- 
ning side by side the whole length of the original canal, usually for 
upwards of a thousand miles, of the same size throughout, and abso- 
lutely parallel to each other. The pair may best be likened to the 
twin rails of a railroad track. The regularity of the thing is startling.' 

Many double canals are shown in the sixth figure on page 358. Aver- 
age distance between the twin canals is 150 to 200 miles. This phe- 
nomenon, still a mystery, does not appear to be an effect of either 
optical illusion or double refraction ; but rather a really double exist- 
ence, seen only under exceptionally favorable conditions of atmosphere. 
More strangely still, the oases too are occasionally seen to be double. 

Meaning of Canal and Oasis. — It is the design of physical science 
not only to record but to explain appearances ; and the canals, whether 
double or single, have, to many astronomers who have seen them, a 
look of artificiality rather than naturalness. If we accept the former, 
the explanation of the canals themselves, advanced by W. H. Pickering 
and reinforced by the argument of Lowell, seems very plausible : 
water is scarce on the planet ; with melting of the polar caps, it is grad- 
ually conducted along narrow channels through the middle of the 
canals, thereby irrigating areas of great breadth which, with the ad- 
vance of the season, become clothed with vegetation. Similarly the 
oases ; and at our great distance, it is vegetation which, although invis- 
ible in the Arean winter, grows visible as canal and oasis with every 
return of spring. The fact that oases are seen only at junctions of 
canals, and not elsewhere, greatly strengthens this argument. Of 
course, acceptance of this theory implies that Mars in ages past, has 
been, and may be still, peopled by intelligent beings ; and that continu- 
ation of their existence upon that planet, during secular dissipation of 
natural water supply, has rendered extensive irrigation a prime requisite. 
For animal life, of types known to us, is dependent upon vegetable life ; 
which, in turn is conditional upon water distribution, either natural or 
artificial. But only by long continued observation of the behavior of 
canal and oasis in both hemispheres of Mars, can we hope for a rational 
solution of the question of life in another world than ours. Such 
difficult research Lowell and his able corps of observers are now faith- 
fully prosecuting with a 24-inch Clark telescope in favorable skies. 

Seasonal Changes. — Striking seasonal changes seen to 
keep step with progress of Mars in his orbit, are best ex- 
hibited by direct comparison between drawings at intervals 
of several months. Three such are chosen in plate vi. The 
region known as Hesperia is central in all. The first, 7th 



Discoveries of Small Planets 361 

June, 1894, corresponds to early spring on Mars. South 
polar snows have just begun to melt. Everywhere encir- 
cling it is the dark area, as if water from the melting of the 
cap; for this band follows the cap as it shrinks, becom- 
ing less in width as the cap grows smaller. This is shown 
in the middle disk, which corresponds to early summer. 
Mark the other changes in the disk: (i) the general thin- 
ning out of dark areas which on the actual planet are 
greenish-blue ; (2) the increase in intensity of reddish 
ochre regions through the southern hemisphere, as if the 
water had in considerable part evaporated, Hesperia 
already beginning to show as an oblique, V-shaped, red- 
dish marking in the center of the disk; (3) progress in 
development of canals, though not as yet far advanced. 
As the planet approaches late summer, in the third draw- 
ing, Hesperia has become a broad cleft through the water 
area, three canals are particularly well developed in the 
northern hemisphere, and the south polar cap has practi- 
cally vanished. In other longitudes like changes went on 
simultaneously, and in the same significant and seemingly 
obvious direction. 

Discoveries of Small Planets. — In 1800, the closing year 
of the eighteenth century, conspicuous absence of a planet 
between Mars and Jupiter as required by Bode's law, led to 
an association of 24 astronomers intent upon search for 
the missing body. Piazzi of Sicily inaugurated the long 
list of discoveries by finding the first one on the first night 
of the 19th century (ist January, 1801). He called it 
Ceres, that being the name of the tutelary divinity of 
Sicily. Three others, named Pallas, Juno, and Vesta, 
were found by 1807, but the fifth was not discovered till 
1845. 

Since 1847 1^0 year has failed to add at least one to the number, and 
in 1896 the increase was 40. The total number is now approaching 



362 The Planets 

500. Of these, 75 were discovered in the United States, mainly by Peters 
(48) at Clinton, New York, and Watson (22) at Ann Arbor, Michigan. 
Palisa, of Vienna, found no less than 72. In 1891, Wolf of Heidelberg 
inaugurated discoveries of these bodies by the aid of photography, 
and he has discovered about 60 in this manner : a sensitive plate ex- 
posed for two or three hours to a suspected region of sky makes a per- 
manent record of all the stars as round disks, and of any small planets 
as short trails because of their apparent motion during exposure. So 
they are discovered about 20-fold more readily than by the old-fash- 
ioned method at the eyepiece of a telescope. Charlois of Nice has 
found nearly 90 small planets by photography. About 100 of the more 
recent discoveries are yet without names, and are designated by their 
number, thus (jii) ; also by a double letter and year of discovery, as 
1897 DE = (42s). Probably there are hundreds more, and possibly thou- 
sands. Discoveries are disseminated by Ritchie's international code. 

Orbits and Origin of Small Planets. — The orbits of 
small planets, although linked together inseparably, still 
present wide degrees of divergence. They are by no 
means evenly distributed : in those regions of the zone 
where a simple relation of commensurability exists between 
the appropriate period of revolution and the periodic time 
of Jupiter, gaps are found, resembling those shown farther 
on as existing in the ring of Saturn. 

Especially is this true for distances corresponding to one half and one 
third of Jupiter's period. Not only are the orbits of small planets far 
from concentric, but they are inclined at exceptionally large angles to the 
ecHptic, that of Pallas (2) being 35°. Several groups exist having a 
near identity of orbits, one such group including 11 members. Poly- 
hymnia (5?) is much perturbed by the attraction of Jupiter, and its mo- 
tion has recently been employed by Newcomb in finding anew the mass 
of the giant planet, equal to ^—^ that of the sun. Victoria (12), Sappho 
(so), and others, on account of favorable approach to the earth, have been 
very serviceable in the hands of Gill and Elkin in helping to ascertain 
sun's distance from earth. Data concerning orbits of these bodies are 
published each year in the Bej'liner Astronomisches Jahrbiich. 

Olbers early originated the theory, now disproved, that 
small planets had their origin in explosion of a single 
great planet. Most probably, however, proximity of so 



The Stir face of f tip iter 



363 



massive a planet as Jupiter 
is responsible for the exist- 
ence of a multitude of small 
bodies in lieu of one larger 
one ; for his gravitative action 
upon the ring in its early 
formative stage, in accord- 
ance with principles of the 
evolution of planets may 
readily have precluded ulti- 
mate condensation of the 
ring into a separate planet. 
Surface of Jupiter. — In a 
telescope of even moderate 
size, Jupiter appears, as in 
this typical view, striped with 
many light and dark belts, 
of varying colors and widths, 
lying across the disk parallel 
to each other and to his equa- 
tor, or nearly so. They al- 
ways appear practically 
straight because the plane 
of Jupiter's equator always 
passes very nearly through 
the earth. The belts are not 
difficult to see ; but the tele- 
scope had been invented 20 
years before they were dis- 
covered, at Rome, in 1630. 
Usually the equatorial zone, 
about 25° broad, is lightest in 
hue, and almost centrally 
through it runs a very narrow 




Jupiter in 1889 iKeeler) 



364 



The Planets 



dark stripe. Larger telescopes reveal a variety of spots 
and streaks in this zone, and permanence of markings is 
rather the exception than the rule. It appears to be a 
region of great physical commotion. Bordering this zone, 
on either side, are usually two broad reddish belts, about 
20° of latitude in width. These are zones of little dis- 
turbance, but the southern one often appears divided. 

Just beyond it is the * great 
red spot.' Here and there 
white cloudlike masses, near 
the edge of the equatorial 
zone, appear to flow over into 
the red belts as long oblique 
streamers, seemingly dividing 
these broad zones into two or 
three narrow stripes. Farther 
from the equator are still other 
belts, growing narrower as the 
poles are approached, because 
curvature of the spherical sur- 
face foreshortens them; and 
all around the limb, whether 
at poles or equator, the belts 
fade into indistinctness. Color 
Jupiter's Great Red Spot in 1881 and ^^d intensity of the principal 

1885 (Denningf) ^ r r 

belts are by no means con- 
stant, their hue being at times brownish, copper-colored, 
and purple. Of the two hemispheres, the reddish tint of 
the southern is rather more pronounced. 

Jupiter's Great Red Spot. — Probably this gigantic mark- 
ing, whose area exceeds that of our whole earth, has long 
been forming ; for although it was not certainly seen until 
1869, and still more definitely in 1878 first by Pritchett, there 
are indications that Cassini, at Paris, observed it in 1685. 




A Chart of Jupiter 



365 



The opposite illustrations show its appearance in 1881 and 1883. 
Breadth of this elliptic marking was about 8000 miles, and length 30,000. 
The great red spot has not been uniformly conspicuous, for it nearly 
faded out in 1883-84. The year following a white cloud appeared to 
cover the middle, making it look like a chain-link. The lowest drawing 
(page 363) shows its appearance in 1889. Now quite invisible, it may 
have a periodicity, and again reappear. Cloud markings near it have 
been observed to be strikingly repelled. If the spot remained station- 
ary upon the planet's surface, it might be simply a vast fissure in the 
outer atmospheric envelope of Jupiter, through which are seen dense 
red vapors of interior strata, if not the planet's true surface ; but its 
slow drift precludes this theory. No satisfactory explanation of the 
great red spot has yet been advanced. 

A Chart of Jupiter. — Notwithstanding considerable variations in 
detailed appearance of Jupiter's disk, many larger markings present a 




'24(? 270 300 330 30 60 

Approximate Chart of a Portion of Jupiter in 1895 (Henderson) 



sufficient permanence from month to month to admit of charting. 
Adjacent is such a chart, on the Mercator projection, and intended 
to be accurate as to general features only. Center of the great red 
spot is taken as origin of longitudes. The principal belts and the more 
important white spots are clearly indicated. From the construction 
of many such charts, at intervals of about a year, much can be learned 
about the planet's atmosphere, present physical condition, and future 
development. As yet photography, successfully applied by Common, 
and Russell, and at the Lick Observatory, although showing accurately 
a great quantity of detail, including a multitude of white and dark spots, 
does not equal the eye in recording finer markings. Length of expo- 
sure and unsteadiness of atmosphere are the chief obstacles. Hough 



366 



The Planets 



in America and Williams in England have been constant students of 
Jupiter. 

Surface of Saturn. — A telescope of only two inches' 
aperture will show the ring of Saturn, also Titan, his larg- 
est satellite. A four-inch object glass will reveal four other 
satellites on favorable occasions. The entire disk appears 
as if enveloped in a thin, faint, yellowish veil. At irregular 




Saturn and his Rings (drawn by Pratt in 1884) 



intervals belts are seen similar to Jupiter's ; but they do not 
persist so long, and are much fainter. As a rule Saturn's 
equatorial belt is his brightest region, and an olive-green 
zone often caps the pole. Excellent photographs have 
been taken at the Lick and Greenwich Observatories. 

At intervals of nearly 1 5 years, the belts appear very much curved, as in 
the illustration above ; because the earth is then about 26° above or 
below the plane of the planet's equator, this being the angle by which 
the axis of Saturn is inclined to a perpendicular to its orbit plane. Mid- 
way between these epochs, the belts appear practically curveless, like 
Jupiter's, because the plane of Saturn's equator is then passing near the 
earth (see drawing opposite on the right). Few bright spots and 



Satunis Rings and their Phases 



367 



irregularities of marking characterize this planet, and his true period of 
rotation is on that account ditScult to ascertain. Celestial photography 
is not yet sufficiently perfected to afford much assistance in recording 
the minute details of so small a disk as Saturn's. With the invention 
of more highly sensitive plates, requiring a much shorter exposure, 
unavoidable blurring of atmosphere will be less harmful. Numerous 
faint and nearly circular dark and white spots or mottlings were 
observed on the ball in 1896. 

Saturn's Rings and their Phases. — Saturn is surrounded 
by a series of thin, circular plane rings which generally 




Very Early Drawings of Saturn 
(in the 1 7th Century) 



Saturn in 1891. (Mark the Excess- 
ive Polar Flattening) 



appear elliptical in form. To astronomers of the first half 
of the 17th century, Saturn afforded much puzzlement, 
and they drew the planet in a variety of fanciful forms, 
some of which are here shown. Huygens first guessed 
the riddle of the rings in 1655. When widely open, 
as in 1884 (opposite page), and in 1898 and 1899, a keen- 
eyed observer, even with a small telescope, can see faint, 
darkish lines or markings near the middle of the ring. 
These are divisions of the system, and there are three 
distinct rings; (^) outer bright ring, (^9) inner bright 
ring, (C) innermost or crape ring. 



368 



The Planets 



1878 



1880 



1882 



1884 



1885 



1886 



1887 



1889 



1891 



1893 



1895 



1897 



1899 



1901 



1903 



1905 



1907 



Phases of the 
Ringf of Saturn 



While Saturn moves round the sun, the ring main- 
tains its own plane constant in direction, just as earth's 
equator remains parallel to itself. Consequently the 
plane of Saturn's rings sometimes passes through the 
earth, sometimes through the sun, and again between 
earth and sun. At these times the rings of Saturn 
actually disappear from view, or nearly so, as just 
illustrated. In the first case, the ring is so thin that 
it cannot be seen when the earth is exactly in the 
plane of it. In the second, the ring disappears be- 
cause the sun is shining on neither side of it, but 
only on its edge. The ring may disappear in the 
third instance when earth and sun are on opposite 
sides of it, and therefore only the unillumined face of 
the ring is turned toward us. Disappearances due to 
these causes take place about every 15 years, or one 
half the periodic time of Saturn, the next occurring 
in 1907, as the adjacent figures (for inverting tele- 
scopes) show. Intervals between disappearances are 
unequal partly because of eccentricity of Saturn's or- 
bit, perihelion occurring in 1885 and aphelion in 1899. 

Size and Constitution of the Rings. — The 

dimensions of the ring system are enor- 
mous, especially in comparison with its 
thickness, which cannot exceed 100 miles. 
Seen edge on, it has the appearance of a 
fine and often broken hair line (page 367). 

Outer diameter of outside ring is 173,000 miles, 
and its breadth, 11,500 miles. Then comes the 
division between the two luminous rings, discovered 
by Cassini in 1676: its breadth is 2400 miles. Outer 
diameter of inner bright ring is 145,000 miles, and its 
breadth, 17,500 miles. Next, the innermost or dusky 
ring, discovered by Bond in 1850: its inner diameter 
is 90,000 miles, and its breadth 10,000 miles ; and it 
joins on the inner bright ring without any apparent 
division. So gauzy is it that the ball of Saturn can 
be seen directly through it, except at the outer edge. 
Characteristic of the inner bright ring is a thickening 
of its outer edge, — much the brightest zone of the 
ring system. The rings of Saturn are neither solid 



The Discovery of Neptuite 369 

nor liquid, but are composed of enormous clouds or shoals of very small 
bodies, possibly meteoric, traveling round the planet, each in an orbit 
of its own, as if a satellite. Perhaps they are thousands of miles apart 
in space ; but so distant is the planet from the earth and so numerous 
are the particles that they present the appearance of a continuous solid 
ring. Keeler has demonstrated by the spectroscope this theory of the 
constitution of Saturn's rings, showing that inner particles move round 
the primary more swiftly than outer ones do, in accord with Kepler's 
third law. The periodic time of innermost particles is 5 h. 50 m., or 
but little more than half the rotation time of the ball itself, which, 
according to some observers, is slightly displaced from the center of 
the rings. Not impossibly the ring system is a transient feature, and 
may be a ninth satellite in process of formation (page 467) . 

Surface of Uranus and Neptune. — The great planet 
Uranus, the first one ever found with the telescope, was 
discovered by Sir William Herschel, 13th March, 1781. 
Calculation backward showed that this planet had been 
observed about 20 times during the century preceding, 
and mistaken for a fixed star. So remote is Uranus and 
so small the apparent disk that very few observers have 
been able to detect anything whatever on his pale green 
surface. Some have seen belts resembling those on 
Jupiter, others a white spot from which a rotation period 
equal to 10 hours was found. More recently the planet 
has been sketched by Brenner, from the clear skies of 
I stria, and six of his drawings are reproduced on the next 
page. The markings appear neither numerous nor defi- 
nite. If so little is found upon Uranus, vastly less must 
be expected from Neptune, and no marking whatever has 
yet been certainly glimpsed. 

The Discovery of Neptune. — The discovery of Neptune 
was a double one. Early in the present century it was 
found that Uranus was straying widely from his theoretic 
positions, and the cause of this deviation was for a long 
time unsuspected. Two young astronomers, Adams in Eng- 
land, and Le Verrier in France, the former in 1843 and the 
todd's astron. — 24 



370 



The Planets 




Uranus in 1896 (Brenner) 



latter in 1845, undertook to find out the cause of this 
perturbation, on the supposition of an undiscovered planet 
beyond Uranus. Adams reached his result first, and 

English astronomers be- 
gan to search for the 
suspected planet with 
their telescopes, by first 
making a careful map 
of all the stars in that 
part of the sky. But 
Le Verrier, on reaching 
the conclusion of his 
search, sent his result 
to the Berlin observatory, where it chanced that an accurate 
map had just been formed of all stars in the suspected 
region. On comparing this with the sky, the new planet, 
afterward called Neptune, was at once discovered, 23d 
September, 1846. It was soon found that Neptune, too, 
had been seen several times during the previous half cen- 
tury, and recorded as a fixed star. The tiny disk, how- 
ever, is readily distinguishable from the stars around it, if a 
magnifying power of at least 200 diameters can be used. 
There are theoretic reasons for suspecting the existence of 
two planets exterior to Neptune ; but no such bodies have 
yet been discovered, although search for them has been 
conducted both optically and by means of photography. 



CHAPTER XIV 

THE ARGUMENT FOR UxXIVERSAL GRAVITATION 

SO Striking a confirmation of Newton's law was 
afforded by the discovery of Neptune, and so com- 
pletely does the universality of that law account for 
the motions of the heavenly bodies, and the variety of their 
physical phenomena, that the present chapter is devoted 
to a partial outline sketch of the argument for universal 
gravitation. 

From Kepler to Newton. — The great progress made by 
Kepler in dealing with the motions of the planets had not 
in any proper sense explained those motions ; for his three 
famous laws merely state hoiv the planets move, without 
at all touching the reason why these laws of their motion 
are true. Before this question could be answered, the 
fundamental principles of physics, or natural philosophy 
as it was called in his day, had to be more fully under- 
stood. These principles concern the state of bodies at 
rest and in motion. Meaning of the term rest is relative, 
and absolute rest is undefinable. Motion is a change of 
place ; and absolute rest is a state of absence of motion. 
Galileo early in the 17th century was the first philosopher 
who ascertained the laws of motion and wrote them down. 
But as they were better formulated by Newton, his name 
is always attached to them. They are axioms, an axiom 
being a proposition whose truth is at once acknowledged 
by everybody, as soon as terms expressing it are clearly 
understood. Newton, indeed, in his great work entitled 

371 



372 Argument for Gravitation 

the Principia^ or principles of natural philosophy, called 
these laws Axiornata^ sive Leges Mo tits. Antecedent to 
proper conception of Newton's law of universal gravitation 
must come an understanding of the three fundamental 
laws of motion. 

Newton's First Law of Motion. — The first law reads as 
follows : Every body continues in its state of rest or of 
uniform motion in a straight line, except in so far as it 
may be compelled by force to change that state. Newton 
asserts in this law the physical truth that a state of uni- 
form motion is just as natural as a state of rest. To one 
who has never thought about such things, this is at first 
very difficult to realize ; because rest seems the natural 
state, and motion an enforced one. But difficulty is at 
once dispelled, as soon as one begins to inquire into the 
causes that stop any body artificially set in motion. 

A baseball rolling upon a level field soon stops because, in moving 
forward, it must repeatedly rise against the attraction of gravity, in 
order to pass over minor obstacles, as grass and pebbles. Also there 
is much surface friction. A rifle shot soon stops because resistance of 
the air continually lessens its speed, and finally gravity draws it down 
upon the earth. A vigorous winter game common in Scotland is called 
curling. The curling stone is a smooth, heavy stone, shaped like a 
much-flattened orange, and with a bent handle on top. When curling 
stones are sent sHding on smooth ice as swiftly as possible, they go for 
long distances with but slight reduction of speed, thus aifording an 
excellent approximation to Newton's first law. But a perfect illustra- 
tion is not possible here on the earth. If it were practicable to project 
a rifle shot into space very remote from the solar system, it would travel 
in a straight path for indefinite ages, because no atmosphere would 
resist its progress, and there is no known celestial body whose attrac- 
tion would draw it from that path. 

Newton's Second Law of Motion, — The second law 
reads : Change of motion is proportional to force applied, 
and takes place in the direction of the straight line in 
which the force acts. 



Newton s Laws of Motion 



Z1Z 



This law is easy to illustrate without any apparatus. Throw a stone 
or other object horizontally. Everybody knows that its path speedily 
begins to curve downward, and it falls to the ground. From the 
smooth and level top of a table or shelf, brush a coin or other small 
object off swiftly with one hand : it will fall freely to the floor a few 




Illustrating Newton's Second Law of Motion 



feet away. Repeat until you find the strength of impulse necessary 
to send it a distance of about two feet, then four, then six feet, as in 
the picture. With the other hand, practice dropping a coin from the 
level of the table, so that it will not turn in falling, but will remain 
nearly horizontal till it strikes the floor. Now try these experiments 
with both hands together, and at the same time. Repeat until one 
coin is released Yrom the fingers at the exact instant the other is 
brushed off the table. Then you will find that both reach the floor at 
precisely the same time ; and this will be true, whether the first coin is 
projected to a distance of two feet, four feet, six feet, or whatever the 
distance. Had gravity not been acting, the first coin would have 
traveled horizontally on a level with the desk, and would have reached 
a distance of two feet, or four feet, proportioned to the impulse. What 
the second law of motion asserts is this : that the constant force (grav- 
ity in this case) pulls the first coin just as far from the place it would 
have reached, had gravity not been acting, as the same force, acting 



374 ArguTneiit for Gravitation 

vertically and alone, would in an equal time draw it from the state of 
rest. Whatever distance the coin is projected^ the 'change of motion' 
is always the vertical distance between the level of table and floor, 
that is, ^ in the direction of the straight line in which the force acts.' 
The law holds good just the same, if the coin is not projected hori- 
zontally, provided the floor (or whatever the coin falls on) is parallel 
to the surface from which it is projected. 

Newton's Third Law of Motion. — The third law reads : 
To every action there is always an equal and contrary 
reaction ; or the mutual actions of any two bodies are 
always equal and oppositely directed. This law com- 
pletes the steps necessary for an introduction to the single 
law of universal gravitation, because it deals with mutual 
actions between two bodies, or among a system of bodies, 
such as we see the solar system actually to be. 

To illustrate in Newton's own w^ords : ' If you press a stone with 
your finger, the finger is also pressed by the stone. And if a horse 
draws a stone tied to a rope, the horse (if I may so say) wdll be equally 
draw^n back toward the stone ; for the stretched rope, in one and the 
same endeavor to relax or unstretch itselt, draws the horse as much 
toward the stone as it drawls the stone toward the horse.' Action and 
reaction are always equal and opposite. 

So when one body attracts another from a distance, the 
second body attracts with an equal force, but oppositely 
directed. If there were two equal, and therefore bal- 
anced, forces acting on but one body^, that would be in equi- 
librium ; but the two forces specified in this third law act 
on two different bodies, neither of which is in equilibrium. 
Always there are two bodies and two forces acting, and 
one force acts on each body. To have a single force is 
impossible. There must be, and always is, a pair of 
forces equal and opposite. Horse and stone advance as a 
unit, because the muscular power of the horse exerted 
upon the ground exceeds the resistance of the stone. 

Transition to the Law of Gravitation. — Having clearly 



Newtoiis Laiu of Gravitation 375 

apprehended the meaning of Newton's three laws of 
motion, transition to his law of universal gravitation is 
easy. The laws of motion, however, must not now be 
thought of separately, but all as applying together and at the 
same time. First, consider the earth in its orbit. Our globe 
has a certain velocity as it goes round the sun ; it w^ould 
go on forever in space in a straight line, with that same 
velocity, except that some deflecting force draws it away 
from that line. This change of motion or direction from a 
straight line must be proportional to the force producing it, 
and the change itself must indicate direction in which 
the force acts ; also, if there is a force acting from the sun 
upon the earth, there must be an equal and oppositely 
directed force from the earth upon the sun, for action and 
reaction are equal. 

Similarly the motion of other planets round the sun ; and 
Newton's reasoning and mathematical calculations, based 
on the law^s of Kepler, made it perfectly clear that planet- 
ary motions might be dependent upon a central force 
directed toward the sun, the intensity of this force grow- 
ing less and less in exact proportion as the square of the 
planet's distance grows greater : thus at twice the distance 
the intensity is but one fourth as great. By making this 
single hypothesis, the meaning of all three laws of Kepler 
was perfectly apparent. But could the action of any such 
force be proved } If it could, the motions of all the satel- 
lites round their primaries might be accounted for by sup- 
posing a like force emanating from the central planets. 
This would mean, too, that the moon must move round us 
obedient to a force directed toward the earth, but decreas- 
ing in intensity just as rapidly as square of moon's distance 
from our center increases. Can it be that the common 
attraction of gravity which draws stones and apples down- 
ward is a force answering to this description } Why 



376 Argument for Gravitation 

should it attract only common objects near at hand ? 
Why may not the realm of this mysterious .force extend 
to the moon ? To the calculation of this problem, New- 
ton next addressed himself. 

Gravitation holds the Moon in her Orbit. — If gravity 
causes the apple to fall from the tree, the bird when shot 
to fall to the ground, and hail to descend from the clouds, 
certainly it is possible, thought Newton, that it may hold 
the moon in her orbit, by continually bending her path round 
the earth. If so, the moon must perpetually be falling 
from the straight line in which she would travel, were the 
central force not acting. Force can be measured by the 
change of place it produces. At the surface of the earth, 
about 4000 miles from the center of attraction, bodies fall 
16. 1 feet in the first second of time. But our satellite is 
240,000 miles away, or 60 times more distant. So the 
moon, if held by the same attraction, only diminishing 
exactly as the square of the distance increases, should fall 
away from a straight line 

of 16. 1 feet; 



(60 X 60) 



that is, 2V ^^ ^^ inch. Newton calculated how much 
the moon actually does curve away from a tangent to 
her orbit in one second, and he found it to be precisely 
that amount (page 237). So the law of gravitation was 
immediately established for the moon ; and Newton's 
subsequent work showed that it explained equally well 
the motion of the satellites of Jupiter round their primary, 
and the motion of earth and all other planets round the 
sun. He found, in fact, that the force acting depends, in 
each case, on the product of the masses of the two bodies, 
and on the square of the distance between them. 

Law of Gravitation extends also to the Planets. — Newton 



Curviliiiear Motion 377 

by no means considered his law of gravitation established, 
just because it explained the motion of the moon round 
the earth. If the law is universal, it must completely 
account for the movements of all known bodies of the 
solar system as well. Since the planets travel round the 
sun as the moon does round the earth, a force directed 
toward the sun must continually be acting upon them. 
Is not this the force of gravitation } Recall Kepler's 
third law. Newton's calculations from it proved that the 
planets fall toward the sun in one second of time through 
a space which is less for each planet in exact proportion as 
the square of its distance from the sun is greater. Also 
Kepler's second law : if the attracting force emanates from 
the sun, the planet's radius vector will pass over equal 
areas in equal times. On the other hand, it cannot pass 
over equal areas in equal times, if the center of attraction 
resides iii any direction but that of the sun. So Kepler's 
second law shows that the force which 
attracts the planets is directed toward 
the sun. What chance for farther doubt 
that this force is the attraction of grav- 
itation of the sun himself } The farther 
Newton's investigations were pushed, Apparatus to illustrate 

^, . M • .1 r j' r 1 • Curvilinear Motion 

the more strikmg the coniirmation or his 
theory. Historically, the three laws of Kepler expressed 
the bare facts of planetary motion, and formed the basis 
upon which Newton built his law of universal gravitation. 
But once this general law was established, it was seen 
that Kepler's laws were immediate consequences of the 
Newtonian law, — merely special cases of the general 
proposition. 

Curvilinear Motion due to a Central Attracting Force. — A facile 
form of apparatus will help to make clear the motion of a body in 
arcs of conic sections under influence of a central attracting force, and 




378 Argument for Gravitation 

to impress it upon the mind. A glass plate about 18 inches in diameter 

is leveled (preceding page) ; and through a central hole projects 

the conical pole-piece of a large electro-magnet. Smoke the upper 

face of the glass plate evenly with lampblack. Connect battery circuit, 

and the apparatus is ready for experiment. Project repeatedly across 

^^ the plate at different velocities a small 

^^^jHfj^^^^^ bicycle ball of polished steel, aimed a 

^^^^■|H|^^^^^^^ little to one side of the pole-piece. It 

^^^^^HH^^^^^^^^L convenient to blow the ball of a 

^^^^^H|j^^^^^P^^^ stout piece of glass tubing, held in the 

^^^K^B^BS^^^^^/I^ plane of the plate. The ball then 

^^^■fl^Bfl^j^^H^^BI leaves its trace upon the plate, as this 

^^H^^B^j^^^B^^H figure shows ; and the form of orbit 

^^B^^KB/^S^K^^K ^ question of initial velocity. 

^^^IH^^^IH^^^^ Lowest speed gives a close approach 

to the ellipse with the pole-piece at 
one of its foci ; friction of the ball in 
Experimental Or^actually obtained ^he lampblack will reduce the velocity 

with this Apparatus SO that the ball is likely to be drawn 

in upon the center of attraction, on 
completing one revolution. A higher speed gives the parabola, whose 
form is also somewhat modified by unavoidable lessening of the balPs 
velocity ; and still higher initial velocities produce the two hyperbolas, 
C and D. This ingenious experiment is due to Wood. The true form 
of all these curves is given on page 397. 

Mutual Attractions. — One farther step had to be taken, 
to apply Newton's third law of motion to the case of sun, 
moon, and planets. This law states that whenever one 
body exerts a force upon another, the latter exerts an 
equal force in the opposite direction upon the first. Earth, 
then, cannot attract moon without moon's also attracting 
earth with an equal force oppositely directed. Sun can- 
not attract earth unless earth also attracts sun in a similar 
manner. So, too, the planets must attract each other; 
and if they do, their motions round the sun must be 
mutually disturbed, in accordance with the second law of 
motion. Kepler's laws, then, must need some slight 
change to fit them to the actual case of mutual attractions. 
But it was known from observation that the planets deviate 



Center of Gravity of Earth-Moon 379 

slightly from Kepler's laws in going round the sun. The 
question, then, arose whether deviations really observed 
are precisely matched by calculated attractions of planets 
upon each other. Newton could not answer this question 
completely, because the mathematics of his day was in- 
sufficiently developed ; but over and over again, refined 
observations of moon and planets since his time have been 
compared with theories of their movements founded on 
Newton's law of universal gravitation, as interpreted by 
the higher mathematics of a later day, until the establish- 
ment of that law has become complete and final. Essen- 
tially everything is accounted for. And unexpected and 
triumphant verification came with the discovery of Nep- 
tune in 1846; for this proved that the law of mutual 
attractions was capable, not only of explaining the motions 
of known bodies, but of pointing out an unknown planet 
by disturbance it produced in the motion of a known and 
neighboring one. 

Earth and Moon revolve round their Common Center of 
Gravity. — It has been said that the moon revolves round 
the earth. This statement needs modification, and it 
admits of ready illustration. Strictly speaking, the moon 
revolves, not round the earth, but round the center of 
gravity of earth and moon considered as a system or unit. 
And as moon's attraction for earth is equal to earth's 
for moon, the center of our globe must revolve round that 
center of gravity also. 

Cut a cardboard figure like that in next illustration — exact size ines- 
sential. Its center of gravity will lie somewhere on the line joining the 
centers of the two disks, and is easily found by trial, puncturing the card 
with a pin until point is found where disks balance each other, and 
gravity has no tendency to make the card swing round. This point 
will be the center of gravity. Around it describe a circle passing 
through center of large disk ; and from the same center describe also 
an arc passing through center of smaller disk. Twirl the card round 



38o 



Argument for Gravitation 



its center of gravity, by means of a pencil or penholder ; or the card 

may be projected into the air, spinning horizontally, and allowed to fall 

to the floor : these circular 
arcs, then, represent paths in 
space actually traversed by 
centers of earth and moon. 
To find where center of grav- 
ity of earth-moon system lies 
in the real earth, recall that 
the mass of our globe is 8i 
times that of the moon. 
Moon's center is therefore 8i 
times as far from center of 
gravity of the system as 
earth's center is. This places 
the common center at a con- 
tinually shifting point always 
within the earth, and at an 
average distance of looo miles 
below that place on its sur- 
face where the moon is in 
the zenith. That the earth 
really does swing round in 
this monthly orbit nearly 

6000 miles in diameter is a fact readily and abundantly verified by 

observation. 




Motion of Center of Gravity of Earth-Moon 



The Newtonian Law of Universal Gravitation. — If this 
attraction for common things, possessed by the earth and 
called gravity, extends to the moon ; if the same force, 
only greater on account of greater mass of central body, 
controls the satellites of Jupiter in their orbits ; if the 
same attraction, greater still on account of the yet greater 
mass of the sun, holds all the planets in their paths 
around him, may it not extend even to the stars } But 
these bodies are so remote that excessive diminution of 
the sun's gravitation, in accordance with the law of inverse 
squares, would render that force so weak as to be unable 
to effect any visible change in their motion, even in thou- 
sands of years. As observed with the telescope, motions 



Gravitation alone Stifficient 381 

of certain massive stars relatively near each other do, 
however, uphold the Newtonian law. No reason, there- 
fore, exists for doubting its sway throughout the whole uni- 
verse of stars. If we pass from the infinitely great to 
the infinitely little, dividing and subdividing matter as far 
as possible, each particle still has weight, and therefore 
must possess power of attraction. Gravity, then, attracts 
each particle to the earth, and in accordance with the 
third law of motion, each particle must attract the earth 
in turn and equally. So the gravitation of earth and 
moon, for example, is really the mutual attraction of all the 
particles composing both these bodies. In its universality, 
then, this simple but all-comprehensive law may finally be 
written : Every particle of matter in the universe attracts 
every other particle with a force exactly proportioned to 
the product of the masses^ and inversely as the square of 
the distance betzveen them. 

Curvilinear Motion : No Propelling Force needed. — 
Newton's theory amounts simply to this : Granted that 
planets and satellites were in the beginning set in motion 
(it does not now concern us in what manner), then the 
attraction of gravitation — of the sun for all the planets 
and of each planet for its satellites — completely accounts 
for the curved forms of their orbits, and for all their 
motions therein. It may be supposed that the state of 
motion was originally impressed upon these bodies by 
a projectile force, or that their present motions are a 
resultant inheritance from untold ages of development 
of the solar system from the original solar nebula, in 
accordance with the working of natural laws. Once set 
in motion, however, Newton's theory suffices to show that 
there is no propelling or other force always pushing from 
behind, nor is the action of any such force at all necessary 
to keep them going. Once started with a certain velocity, 



382 Argument for Gravitation 

the uninterrupted working of gravitation maintains every 
body continually in motion round its central orb. In one 
part of its elliptic path, a planet, for example, may recede 
from the sun, but the sun again pulls it back ; afterward it 
again recedes, but equally again it returns, perihelion and 
aphelion perpetually succeeding each other. Gravitation 
alone explains perfectly and completely all motions known 
and observed. 

Why the Earth does not fall into the Sun. — Draw 
several arrows tangent to the ellipse at different points, 
to show in each case the direction in 
which earth is going when at that 
point. From these points of tangency 
draw dotted lines toward that focus 
where the sun is, to represent direction 
in which gravitation is acting. It is 

Earth is never moving di- . , . . 

rectiy toward the Sun apparent that the planet is never mov- 
ing directly toward the sun, but always 
at a very large angle with the radius vector ; greatest at 
perihelion, B, and aphelion, D, where it becomes a right 
angle. There the sun is powerless either to accelerate or 
retard. According to Kepler's second law, velocity in orbit 
is continually increasing from aphelion to perihelion, be- 
cause gravitation is acting at an acute angle with the direc- 
tion of motion A. Therefore earth's motion is all the time 
accelerated, until it reaches perihelion. Here velocity is a 
maximum, because the sun's attraction has evidently been 
helping it along, ever since leaving aphelion. Gravitation 
of the sun, too, has increased, exactly as the square of the 
planet's distance has decreased. Calculating these two 
forces at perihelion, it is found that earth's velocity makes 
the tendency to recede even stronger than the increased 
attraction of the sun ; so that our planet is bound to pass 
quickly by its nearest point to the sun, and recede again 



Strength of Solar Attraction 383 

to aphelion. On reaching its farthest point, relation of 
the two forces is reversed ; velocity has been diminishing 
all the way from perihelion, because gravitation is acting 
at an obtuse angle with direction of motion, C. The earth 
is all the time retarded, gravitation holding it back, until 
at aphelion its velocity is so much lessened that even the 
enfeebled attraction of the sun overpowers it, and there- 
fore begins to draw the earth toward perihelion again. 
So all the planets are perpetually preserved (i) against 
falling into the sun, and (2) against receding forever 
beyond the sphere of his attraction. At points where 
both these catastrophes at first seem most likely to occur, 
direction of planet's motion is always exactly at right 
angles to the attracting force ; thus is assured that curva- 
ture of orbit requisite to carry it farther away from the 
sun in the one case, and in the other to bring it back 
nearer to him. 

Strength of the Sun's Attraction. — It was shown on page 144 that 
the earth, in traveling 18 V miles, is bent from a truly straight course 
only one ninth of an inch by the sun's attraction. So it might seem 
that the force is not very intense after all. But by calculating it and 
converting it into an equivalent strain on ordinary steel, it has been 
found that a rod or cylinder of this material 3000 miles in diameter 
would be required to hold sun and earth together, if gravitation were to 
be annihilated. Or, if instead of a solid rod, the force of attraction 
were to be replaced by heavy telegraph wires, the entire hemisphere of 
the earth turned toward the sun would need to be thickly covered with 
them, — about 10 to every square inch of surface. But the necessity 
for this vast quantity of so strong a material as steel becomes apparent 
on recalling that the weight of the earth is six sextillions of tons, while 
the weight of the sun is more than 330,000 times greater ; and the stress 
between them is equal to the attraction of sun and earth for each 
other. Gravitation in the solar system must be thought of as pro- 
ducing stresses of this character between all bodies composing it, and 
taken in pairs ; stress between each pair being proportional to the 
product of their masses, and varying inversely as the square of the dis- 
tance separating them varies. Sun disturbs the moon's elliptic motion 
greatly, and even Venus, Mars, and Jupiter perturb it perceptibly. 



384 Argument for Gravitation 

What is Gravitation ? — Distinction is necessary between 
the "i^xxa^ gravity d^nA gravitation. On page 88 it was shown 
that gravity diminishes from pole to equator, on account 
of (i) centrifugal force of earth's rotation, and (2) oblate- 
ness of earth, or its polar flattening, by which all points 
on the equator are further from the center than the poles 
are. Earth's attraction lessened in this manner is called 
gravity. Gravitation, on the other hand, is the term used 
to denote cosmic attraction in accordance with the New- 
tonian law, between all bodies of the universe taken in 
pairs, and depending solely upon the product of the masses 
of each pair and the distance which separates them. Do 
not make the mistake of saying that Newton discovered 
gravity, or even gravitation ; for that would be much like 
saying that Benjamin Franklin discovered lightning. Men 
had always seen and known that everything is held down 
by a force of some sort, and had recognized from the 
earliest times that bodies possess the property called 
weight. What Newton did do, however, was to discover 
the universality of gravitation, and the law of its action 
between all bodies : upon all common objects at the surface 
of the earth ; upon the moon revolving round us ; and upon 
the planets and comets revolving round the sun. This 
cardinal discovery is the greatest in the history of astron- 
omy. Great as it is, however, it is not final ; for Newton 
did not discover, nor did he busy himself inquiring, what 
gravitation is. Indeed, that is not yet known. We only 
know that it acts instantaneously over distances whether 
great or small, and in accordance with the Newtonian law ; 
and no known substance interposed between two bodies 
has power to interrupt their gravitational tendency toward 
each other. How it can act at a distance, without contact 
or connection, is a mystery not yet fathomed. 

Weighing a Planet that has a Satellite. — If a planet has 



Weighing the Planets 385 

a satellite, it is easy to find the mass, or quantity of matter 
in terms of sun's mass. First observe mean distance of 
satellite from its primary, and then find the time of revo- 
lution. Cube the distance of any planet from the sun, and 
divide by square of periodic time ; the quotient will be 
the same for every planet, according to Kepler's third law. 
Also cube the distance of any satellite of Saturn from the 
center of the planet, and divide by the square of its time 
of revolution : the quotient will be the same for every sat- 
ellite, if distances and periodic times have been correctly 
measured. Do the same for satellites of other planets, — 
Mars, Jupiter, Uranus, and Neptune. The quotients will 
be proportional in each case to mass of central body in 
terms of the sun ; in the case of Saturn, for example, the 
quotient for each satellite will be 3-5^1; that for sun and 
planets. The sun, then, is 3501 times more massive than 
Saturn, as found by A. Hall, Jr. Similarly may be found 
the mass of any other planet attended by a satellite. It 
is not necessary to know the mass of the satellite, because 
the principle involved is simply that of a falling body ; and 
we know, in the case of the earth, that a body weighing 
100 pounds or 1000 pounds will fall no swifter than one 
which weighs only 10 pounds. By the same method, too, 
binary stars are weighed (page 454), when their distances 
from each other and times of revolution become known. 

Weighing a Planet that has No Satellite. — This is a 
much more difficult problem ; fortunately only two large 
planets without satellites are known, — Mercury and Venus. 
Their masses can be ascertained only by finding what dis- 
turbances they produce in the motions of other bodies near 
them. The mass of Venus, for example, is found by the 
deviation she causes in the motion of the earth. The mass 
of Mercury is found by the perturbing effect upon Encke's 
comet, which often approaches very near him. The New- 
todd's astron. — 2; 



386 



Argument for Gravitation 



tonian law of gravitation forms the basis of the intricate 
calculations by which the mass is found in- such a case. 
But the result is reached only by a process of tedious com- 
putation and is never certain to be accurate. Much more 
precise and direct is the method of determining a planet's 
mass by its satellite. 

The vast difference between the two methods was illustrated at the 
Naval Observatory, Washington, 1877, shortly after the satellites of 
Mars were discovered. The mass of that planet, as previously esti- 
mated from his perturbation of the earth, was far from right, although 
it had cost months of figuring, based upon years of observation. Nine 
days after the satelHtes were first seen, a mass of Mars very near the 
truth was found by only a half hour's facile computation. 

Weighing the Sun. — In weighing the planets, the sun 
is the unit. Our next inquiry is, what is the sun's own 
weight } How many times does the mass of the sun ex- 
ceed that of the earth } Evidently the law of gravitation 
will afford an answer to this question 
if we compare the attraction of sun 
with that of earth at equal distances. 
At the surface of the earth a body 
falls 16. 1 feet in the first second of 
time. Imagine the sun's mass all con- 
centrated into a globe the size of the 
earth : how far would a body on its 
surface fall in the first second .^ First 
recall how far the earth falls toward 
the sun (or deviates from a straight 
line) in a second : it was found to be 
0.0099 feet (page 144). This is deflec- 
tion produced by the sun at a distance 
of 93,000,000 miles. But we desire to know how far the 
earth would fall in a second, were its distance only 4000 
miles from the sun's center; that is, if it were 23,250 times 




WATER OF 
OPPOSITE TIDE 



WATER OF 
DIRECT TIDE 



To explain the Direct and 
the Opposite Tides 



Explanation of the Tides 387 

nearer. Obviously, as attraction varies inversely as the 
square of the distance, it would fall 0.0099 x [23,250]^, 
or 5,351,570 feet. But we saw that the earth's mass 
causes a body to fall 16. i feet in the first second; there- 
fore the sun's mass is nearly 332,000 times greater than 
that of the earth. 

Gravitation explains the Tides. — According to the 
law of gravitation, the attraction of moon and earth is 
mutual ; moon attracts earth as well as earth attracts 
moon. Earth, then, may be considered also as traveling 
round the moon (page 380). Therefore, earth falls toward 
moon, just as moon in going round earth is continually 
dropping from the straight line in which it would move, 
if gravitation were not acting. Imagine the earth made 
up of three parts (opposite page), independent and free 
to move upon each other : {a) the waters on the side toward 
the moon ; {b) the solid earth itself ; {c) the waters on the 
side away from the moon. In going round moon or sun, 
these three separate bodies would fall toward it, through 
a greater or less space according to their individual dis- 
tance from sun or moon. Waters of the opposite tide, 
therefore, would fall moonward or sunward through the 
least distance, waters of the direct tide through the great- 
est distance, and the earth itself through an intermediate 
distance. The resultant effect would be a separation from 
earth of the w^aters on both near and further sides of it. 
As, however, the real earth and the waters upon it are not 
entirely independent, but only partially free to move rela- 
tively to each other, the separation actually produced takes 
the form of a tidal bulge on two opposite sides. These 
are known as the direct and the opposite tides. 

Tides raised by the Sun. — Besides our satellite the only 
other body concerned in raising tides in the waters of the 
earth is the sun. Newton demonstrated that the force 



388 



Arg2ifnent for Gravitation 



which raises tides is proportional to the difference of 
attractions of the tide- raising body on two opposite sides 
of the earth. Also he showed that this force becomes less 
as the cube of the distance of tide-producing body grows 
greater. It is, therefore, only a small portion of the whole 
attraction, and the sun tide is much exceeded by that of the 
moon. To ascertain how much : first as to masses merely, 
supposing their distances equal, sun's action would be 





HIGHEST TIDE 




HIGHEST TIDE 



HIGHEST TIDE 



LOWEST 
TIDE 




LOWEST 
TIDE 



HIGHEST TIDE 



FULL Q MOON 

Spring Tide at Full Moon 



Spring Tide at New Moon 



26\ million tim.es that of . moon, because his mass is 
8 1 X 332,000 times greater. But sun's distance is also 
390 times greater than the moon's ; so that 

26 V millions 
(390)3 

expresses the ratio of sun tide to moon tide, or about the 
relation of 2 to 5. 

Sun Tides and Moon Tides combined. — As each body 
produces both a direct and an opposite tide, it is clear that 
very high tides must be raised at new moon and at full 
moon, because sun and moon and earth are then in line. 



L u n i-Sola r Tides 



389 



These are spring tides (or high-rising tides), occurring, as 
the figures opposite show, twice every lunation. Similarly 
is explained the formation of lesser tides, called neap 
tides, which occur at the moon's first and third quarters. 
Instead of conspiring together to raise tides, the attraction 
of the sun acts athwart the moon's, so that the resultant 
neap tides are raised by the difference of their attractions, 
instead of the sum. Both relations of sun, moon, and 





riRST f-^ MEDIUM 

quarterI^ high TID 




LOW TIDE 

Neap Tide at First Quarter 




Neap Tide at Last Quarter 



earth producing such tides are shown. Considering only 
average distances of sun and moon, spring tides are to 
neap tides about as 7 to 3. For the earth generally, 
highest and lowest spring tides must occur when both sun 
and moon are nearest the earth ; that is, when the moon 
at new or full comes also to perigee, about the beginning 
of the calendar year. The complete theory of tides can 
be explained only by application of the higher mathe- 
matics. But the law of gravitation, taken in connection 
with other physical laws, fully accounts for all observed 
facts ; so that the tides form another link in the chain 
of argument for universal gravitation. 



390 Argument for Gravitation 

The Cause of Precession. — Precession and its effect upon 
the apparent positions of the stars have already been de- 
scribed and illustrated in Chapter vi. This peculiar behav- 
ior of the earth's equator is due to the gravitation of sun 
and moon upon the bulging equatorial belt or zone of the 
earth, combined with the centrifugal force at the earth's 
equator. As equator stands at an inclination to ecliptic, 
this attraction tends, on the whole, to pull its protuberant 
ring toward the plane of the ecliptic itself. But the earth's 
turning on its axis prevents this, and the resultant effect is 
a very slow motion of precession at right angles to the 
direction of the attracting force, similar to that exemplified 
by attaching a small weight to the exterior ring of a 
gyroscope. Three causes contribute to produce preces- 
sion : if the earth were a perfect sphere, or if its equator 
were in the same plane with its path round the sun (and 
with the lunar orbit), or if the earth had no rotation on 
its axis, there would be no precession. The action of 
forces producing precession is precisely similar to that 
which raises the tidal wave ; and, accordingly, solar pre- 
cession takes place about two fifths as rapidly as that pro- 
duced by the moon. The slight attraction of the planets 
gives rise to a precession -^^ that of sun and moon. 

Nutation of the Earth^s Axis. — Nutation is a small and periodic 
swinging or vibration of the earth's poles north and south, thereby 
changing declinations of stars by a few seconds of arc. The axis of 
our globe, while traveling round the pole of the ecliptic, A, has a slight 
oscillating motion across the circumference of the circle described by 
precession. So that the true motion of the pole does not take place 
along pp'^ an exact small circle around ^ as a pole, but along a wavy 
arc as shown in next illustration. The earth's pole is at P only at a 
given time. This iiodding motion of the axis, and consequent undu- 
lation in the circular curve of precession, is called nutation. The 
period of one cross oscillation due to lunar nutation is i8i years, so 
that the number of waves around the entire circle is greatly in excess 
of the proportion represented in the figure. In reality there are nearly 



Nutation Illustrated 



391 



1400 of them. Just as the celestial equator glides once round on the 
ecliptic in 25,900 years, as a result of precession, so the moon's orbit 
also slips once round the ecliptic in i8f years, thereby changing 
slightly the direction of moon's attraction upon the equatorial pro- 
tuberance of our earth, and producing nutation. 




Illustrating Motion of the Celestial Pole by Nutation 



When Newton had succeeded in proving that his law of 
universal gravitation accounted not only for the motions of 
the satellites round the planets, for their own motions 
round the sun, for the rise and fall of the tides, and for 
those changes in apparent positions of the stars occa- 
sioned by precession and nutation, evidence in favor of 
his theory of gravitation became overwhelming, and it was 
thenceforward accepted as the true explanation of all celes- 
tial motions. 



CHAPTER XV 

COMETS AND METEORS 

COMETS, as well as other unusual appearances in the 
heavens, were construed by very ancient peoples 
into an expression of disapproval from their deities. 
* Fireballs flung by an angry God,' they were for centuries 
thought to be 'signs and wonders,' — a sort of celestial 
portent of every kind of disaster. The downfall of Nero 
was supposed to be heralded by a comet ; and for centuries 
the densest superstition clustered about these objects. 

True Theory of Comets not Modern. — Chaldean star- 
gazers were apparently the sole ancient nation to regard 
comets as merely harmless wanderers in space. The 
Pythagoreans only, of the old philosophers, had some 
general idea that they might be bodies obeying fixed laws, 
returning perhaps at definite intervals. 

Seneca held this view, and Emperor Vespasian attempted to laugh 
down the popular superstitions. But in those days, far-seeing utter- 
ances had little effect upon a world full of obstinate ignorance. Some 
of the old preachers proclaimed that comets are composed of the sins 
of mortals, which, ascending to the sky, and so coming to the notice of 
God, are set on fire by His wrath. Texts of Scripture were twisted 
into apparent proofs of the supernatural character of comets, and for 
seventeen centuries beliefs were held that fostered the worst forms of 
fanaticism. Copernicus, of course, refused to regard comets as super- 
natural w^arnings, but the i6th century generally accepted their evil 
omen as a matter of course. By the middle of the 17th century came 
the dawn of changing view^s, although even as late as the end of that 
century, knowledge of the few facts known about comets was kept so 
far as possible from students in the universities, that their religious 
beliefs might not be contaminated. 

392 



Discoveries of Comets 



393 




A Comet is discovered by its Motion 



But credence began to be given to the statements of 
Tycho Brahe and Kepler that comets were supralunar, or 
beyond the moon, and perhaps not so intmiately concerned 
m 'war, pestilence, and fam- 
ine ' as had been believed. 
Newton farther demonstrated 
that comets are as obedient to 
law as planets ; and with his 
authoritative statements came 
the full daylight of the modern 
view. 

Discoveries of Comets. — 
Comets are nearly all dis- 
covered by apparent motion 
among the stars. The illustra- 
tion shows the field of view of a telescope, in which ap- 
peared each night two faint objects. Upper one remained 
stationary among the stars, but lower one was recognized 

as a comet because it moved, 
as the arrow shows, and was 
seen each night farther to 
the right. A century ago, 
Caroline Herschel in Eng- 
land, and Messier in France, 
were the chief discoverers of 
comets. Pons discovered 30 
comets in the first quarter of 
the 19th century. 

Among other noteworthy Euro- 
pean ^ comet-hunters ' during the 
middle and latter half of this cen- 
tury were Brorsen, Donati, and 
Tempel. In America, Swift, 
Brooks, and Barnard have been preeminently successful. Between 
them and several other astronomers, both at home and abroad, the 




Early View of Donati's Comet U 858) 



394 



Comets and Meteors 



entire available night-time sky is parceled out for careful telescopic 
search, and it is not Hkely that many comets, at all within the range 

of visibility from the earth, escape their 
critical gaze. Sweeping for comets is 
an attractive occupation, but one re- 
quiring close application and much 
patience. Large and costly instruments 
are by no means necessary. Messier 
discovered all his comets with a spy- 
glass of 2\ inches diameter, magnify- 
ing only five times ; and the name of 
Pons, the most successful of all comet- 
hunters, a doorkeeper at the observa- 
tory of Marseilles, is now more famous 
in astronomy than that of Thulis, the 
then director of that observatory, who 
tauo^ht and encourao^ed him. 




Telescopic Comet without and with 
Nucleus 




Halley's Comet (1835) 



Their Appearance. — Usually a 
comet has three parts. The 
micleics is the bright, star-like 

point which is the kernel, the true, potential comet. 

Around this is spread the coma, a sort of luminous fog, 

shading from the nucleus, and 

forming with it the head. Still 

beyond is the delicate tail, 

stretching away into space. 

And this to the world in gen- 
eral is the comet itself, though 

always the least dense of the 

whole. Sometimes entirely 

wanting, or hardly detectible, 

the tail is again an exten- 
sion millions of miles long. 

Although usually a single 

brush of light, comets have 

been seen with no less than 

SIX tails. ^^^^ Qf Donati's Comet (1858) 




Development of the Tail 



395 



Changes in Appearance. — With increase in a comet's 
speed on approaching the sun and its state of excitation, 
perhaps electrical, its physical appearance changes and 
develops accordingly. When 
remote from the sun, comets are 
never visible except by aid of a 
telescope, and their appearance 
is well shown at top of oppo- 
site page ; but on approaching 
nearer the sun, a nucleus will 
often develop and throw off jets 
of luminosity toward the sun, 
sometimes curving round and 
opening like a fan. On rare 
occasions the comet will become 
so brilliant as to be visible in 
broad daylight. After growth 
of the coma comes development 
of the tail ; and this showy 
appendage sometimes reaches 
stupendous lengths, even so 
great as sixty millions of miles, 
growing often several million 
miles in a day. 

Development and Direction of 
Tail. — It is not a correct anal- 
ogy that the tail streams out 
behind like a shower of sparks 
from a rocket. There is no 
medium to spread the tail ; for there is no material sub- 
stance like air in interplanetary space, and therefore noth- 
ing to sweep the tail into the line of motion. Explanation 
of the backward sweep of the tail, nearly always away 
from the sun, as in above diagram, is found in the fact that 




Tail always points away from the Sun 



396 



Comets and Meteors 



while the comet is attracted, the tail is probably repelled 
by the sun. Rapid growth of tail upon approaching the 
sun is explainable in this way : the comet as a solid is 
attracted ; but when it comes near enough to be partly 
dissipated into vapor, the highly rarefied gas is so repelled 
that gravitation is entirely overcome, and the tail streams 
visibly away from the sun, as long as it is near enough to 
have part of its substance continually turning into vapor. 
Receding, the great heat diminishes ; and the tail becomes 
smaller, because less material is converted into vapor. 

Types of Cometary Tails. — Bredichin divides tails of 
comets into three types: (i) those absolutely straight in 

space, or nearly so, like the 
tail of the great comet of 
1843 ; (2) tails gently curved, 
like the broad streamer of 
Donati's comet of 1858 (page 
20); (3) short bushy tails, 
curving sharply round from 
the comet's 'nucleus, as in 
Encke's comet. The origin 
of tails of the first type is 
related to ejections of hy- 
drogen, the lightest element 
known, and the sun's repul- 
sive force is in this case 14 
times stronger than his gravi- 
tative attraction. The slightly 
curved tails of the second type are due to hydrocarbons 
repelled with a force somewhat in excess of solar gravity. 
In producing the sharply curved tails of the third type, 
the sun's repellent energy is about one fifth that of his 
gravity, and these tails are formed from emanations of still 
heavier substances, principally iron and chlorine. 




Types of Cometary Tails iBredichin) 



Cometary Orbits 



397 



This theory permits a complete explanation of a comet's possessing 
tails of two different types ; or even tails of all three distinct types. 
Hussey's fine photograph of comet Rordame-Quenisset (1893) showed 
four tails, which subsequently condensed into a single one. Evidently 
the ejections may be at different times connected with hydrogen, hydro- 
carbon, or iron, or any combination of these, according to the chemi- 
cal composition of substances forming the nucleus. 

Observations for an Orbit. — As soon as a new comet is 
discovered, its position among the stars is accurately ob- 
served at once. On subsequent evenings, these observa- 
tions are repeated ; and after 
three complete observations have 
been obtained, the precise path 
of the comet can generally be 
calculated. This path will be 
one of the three conic sections : 
(i) if it is an ellipse, the comet 
belongs to the class of periodic 
comets, and the length of its 
period will be greater as the 
eccentricity of orbit is greater ; 

(2) if the path is a parabola, the 

comet will retreat from the sun along a line nearly par- 
allel to that by which it came in from the stellar depths ; 

(3) if a hyperbola, the paths of approach to and recession 
from the sun will be widely divergent. 

Cometary Orbits. — Some comets are permanent members 
of the solar system, while others visit us but once. Three 
forms of path are possible to them, — the ellipse, the 
parabola, and the hyperbola. With a path of the first type 
only can the comet remain permanently attached to the 
sun's family. The other two are open curves, as in above 
diagram ; and after once swinging closely round the sun, 
and saluting the ruler of our solar system, the comet then 
plunges again into unmeasured distances of space, 




Form of Cometary Orbits 



398 



Comets and Meteors 



Whether or not an orbit is a closed or open curve depends entirely 
upon velocity. If, when the comet is at distance unity, or 93,000,000 
miles from the sun, its speed exceeds 26 miles a second, it will never 

come back; if less, it will 
return periodically, after wan- 
derings more or less remote. 
Very often the velocity of a 
comet is so near this critical 
value, 26 miles a second, that 
it is difficult to say certainly 
whether it will ever return or 
not. Many comets, however, 
do make periodical visits 
which are accurately foretold. 
The form and position of 
their orbits show in numer- 
ous instances that these 
comets were captured by 
planetary attraction, which 
has reduced their original 
velocity below 26 miles a sec- 
ond, and thus caused them 
to remain as members of the 
solar system indefinitely, and 
obedient to the sun^s control. 
A Projectile's Path is a 
Parabola. — This proposition, 
demonstrated mathematically 
from the laws of motion, is excellently verified by observation of the 
exact form of curves described by objects thrown high into the air. 
Resistance of the atmosphere does not affect the figure of the curve 
appreciably, unless the velocity is very swift. A ' foul ball ^ frequently 
exhibits the truth of this proposition beautifully, in its flight from the 
bat, high into the air, and then swiftly down to the * catcher,^ wdiom 
the photograph shows in the act of catching the ball, though some- 
what exaggerated in size. The horizontal line above the parabola is 
called the directrix^ and the vertical line through the middle of the 
parabola is its axis. One point in the axis, called the focus, is as far 
below the vertex as the directrix is above it. This curve has a number 
of remarkable properties, one of which is that every point in the curve 
is just as far from the focus as it is perpendicularly distant from the 
directrix (shown by equality of the dotted lines). Another property, 
very important and much utilized in optics, is this : from a tangent at 
any point of the parabola, the line from this point to the focus makes 




A Projectile's Path is a Parabola 
(From an Instantaneous Photograph by Lovell) 



Tlie Periodic Comets 399 

the same angle with the tangent that a Une drawn from the point of 
tangency parallel to the axis does. According to this property, parallel 
rays all converge to the focus of a reflector (page 196). 

Direction of their Motion. — Unlike members of the solar 
system in good and regular planetary standing, comets 
move round the sun, some in the same direction as the 
planets ; others revolve just opposite, that is, from east 
to west. The planes of cometary orbits, too, lie in all di- 
rections — their paths may be inclined as much as 90° to 
the ecliptic. A comet can be observed from the earth, 
and its position determined, only while in that part of its 
orbit nearer the sun. Generally this is only a brief interval 
relatively tt) the comet's entire period, because motion 
near perihelion is very swift. It is doubtful whether any 
comet has ever been observed farther from the sun than 
Jupiter. 

Dimensions of Comets. — Nucleus and head or coma of 
a comet are the only portions to which dimension can 
strictly be assigned. There are doubtless many comets 
whose comae are so small that we never see them — prob- 
ably all less than 15,000 miles in diameter remain undis- 
covered. The heads of telescopic comets vary from about 
25,000 to 100,000 miles in diameter ; that of Donati's comet 
of 1858 was 250,000 miles in diameter, and that of the 
great comet of 181 1, the greatest on record, w^as nearly five 
times as large. Tails of comets are inconceivably exten- 
sive, short ones being about 10,000,000 miles long, and the 
longest ones (that of the comet of 1 882, for example) exceed- 
ing 100,000,000. To realize this prodigious bulk, one must 
remember that if such a comet's head were at the sun, the 
tail would stretch far outside and beyond the earth. 

The Periodic Comets. — Comets moving round the sun 
in well-known elliptic paths are called periodic comets. 
About 30 such are now known, with periods less than lOO 



400 Comets and Meteors 

years in duration, the shortest being that of Encke's comet 
(3^ years), and the longest that of Halley's (about 76 years ). 
Nearly all of these bodies are invisible to the naked eye, 
and only about half of them have as yet been observed at 
more than a single return. Nearly as many more comets 
travel in long oval paths, but their periods are hundreds or 
even thousands of years long, so that their return to peri- 
helion has not vet been verified. 

Planetary Families of Comets. — When periodic comets 
are classified according to distance from the sun at their 
aphelion, it is found that there is a group of several corre- 
sponding to the distance of each large outer planet from 
the sun. Of these, the Jupiter family of comets is the 
most numerous, and the orbits of many of them are ex- 
cellently shown on the opposite page. Without much 
doubt, these comets originally described open orbits, either 
parabolas or hyperbolas; but on approaching the sun, they 
passed so near Jupiter that he reduced their velocity below 
the parabolic limit, and they have since been forced to 
travel in elliptical orbits, having indeed been captured by 
the overmastering attraction of the giant planet. While 
Jupiter's family of comets numbers 18, Saturn similarly 
has 2, Uranus 3, and Neptune 6. 

Groups of Comets. — Vagaries in structure of comets 
prevent their identification by any peculiarities of mere 
physical appearance. Identity of these bodies then, or 
the return of a given comet, can be established only by 
similarity of orbit. In several instances comets have made 
their appearance at irregular intervals, traveling in one 
and the same orbit. They could not be one and the same 
comet; so these bodies pursuing the same track in the 
celestial spaces are called groups of comets. 

The most remarkable of these groups consists of the comets of 1668, 
1843, 1880, 1882, and 1887, all of which travel taiideni round the sun. 




Jupiter's Family of Comets. (From Professor Payne's Popular Astronomy^ 
TODD'S ASTRON. — 26 4OI 



402 



Comets and Meteors 



Probably they are fragments of a comet, originally of prodigious size, 
but disrupted by the sun at an early period in its history ; because the 
perihelion point is less than 500,000 miles from the sun's surface. At 
this distance an incalculably great disturbing tidal force would be ex- 
erted by the sun upon a body having so minute a mass and so vast a 
volume ; and separate or fragmentary comets would naturally result. 

Number of Comets. — In the historical and scientific 
annals of the past, nearly 1000 comets are recorded. Of 
these about 100 were reappearances ; so that the total num- 
ber of distinct comets known and observed is between 800 
and 900. 

During the centuries of the Christian era preceding the eighteenth, the 
average number was about 30 each century ; but nearly all these were 
bright comets, discovered and observed without telescopes. As tele- 
scopes came to be used more and more, 70 comets belong to the eigh- 
teenth century, and nearly 300 to the 
nineteenth. Of this last number, less 
than one tenth could have* been discov- 
ered with the naked eye ; so that the 
number of bright comets appears to 
vary but little from century to century. 
The number of telescopic comets found 
each year is on the increase, because 
more observers are engaged in the 
search than formerly, and their work is 
done in accordance with a carefully 
organized system. About seven com- 
ets are now observed each year. Fewer 
are found in summer, owing to the 
short nights. During the 2000 years 
— although but ^ a minute in the prob- 
able duration of the solar system' — 
the comets coming within reach of the sun must be counted by thou- 
sands ; for it is probable that about 1000 comets pass within visible 
range from the earth every century. It is not, however, likely that 
more than half of these can ever be seen . 

Remarkable Comets before 1850. — Comets of immense proportions 
have visited our skies since the earliest times. Others having singular 
characteristics must be mentioned also. Halley's comet is famous 
because it was the first whose periodicity was predicted. This was in 
1704, but the verification did not take place till 1759, again in 1835, 




Cheseaux's Multi-tailed Comet 
K 1 744) 



The Lost Biela s Comet 403 

and it will reappear in 1910. The comet of 1744 (opposite) had a 
fan-shaped, multiple tail. The great comet of 181 1 was one of the finest 
of the 19th century, and its period is about 3000 years in duration. In 
1 8 18 Pons discovered a very small comet, which has become famous 
because of the short period of its revolution round the sun — only 3J 
years. This fact was discovered by Encke. a great German astronomer, 
and the comet is now known as Encke's comet. It has been seen at 
every return to perihelion, three times every ten years. Up to 1868, 
the period of Encke's comet was observed to be shortening, by about 
2j hours, at each return ; and this diminution led to the hypothesis 
of a resisting medium in space — not well sustained by more recent 
investigations. Encke's comet is inconspicuous, has exhibited remark- 
able eccentricities of form and structure, and is now invisible without 
a telescope. Returns are in 1895, 1898, and 1901. The great comet 
of 1843, perhaps the most remarkable of all known comets, was visible 
in full daylight, and at perihelion the outer regions of its coma must 
have passed within 50,000 miles of the surface of the sun — nearer than 
any known body. At perihelion, its motion was unprecedented in 
.swiftness, exceeding 1,000,000 miles an hour. Its period is between 500 
and 600 years. 

The Lost Biela^s Comet. — Montaigne at Limoges, France, discov- 
ered in 1772 a comet which was seen again by Pons in 1805, and then 
escaped detection until 1826, when it 

was rediscovered and thought to be HHIIHH^HH^HHI 
new by an Austrian officer named Biela, ^|r -^^^HI^^^^^H 
by whose name the comet has since ^^K C ^^flj^^^^^^^H 
been know^n. He calculated its orbit, ^^■^^^^^^^!^P|^H 
and showed that the period was 6^ ^^^^^^H^HHI^^^H 
years. At reappearance 1845-46, ^^^^H^^^^^|^^H|H 
seen to have pi^^^^^^^^^^^^^H 

unequal fragments, as in the illustra- ■^BHJ^^^I^^H^H 
tion, and their distance apart had Biela's Double Comet (1845-46) 
greatly mcreased when next seen in 

1852. At no return since that date has Biela's comet been seen; and 
the showers of meteors observed near the end of November in 1872, 
1885, and 1892, are thought to be due to our earth passing near the 
orbit of this lost body, and to indicate its further, if not complete dis- 
integration. These meteors are, therefore, known as the Bielids : also 
Andromedes, because they appear to come from the constellation 
of Andromeda. During the shower of 1885, on the 27th of Novem- 
ber, a large iron meteorite fell, and was picked up in Mazapil. Mexico. 
Without doubt it once formed part of Biela's comet. 

Remarkable Comets between 1850 and 1875. — In 1858 appeared 
Donati's comet, which attained its greatest brilliancy in October, having 



404 



Comets and Meteors 



a tail 40° long, sharply curved, and 8° in extreme breadth. Also there 
were two additional tails, nearly straight, and very long and narrow, 
as shown in the following illustration. Its orbit is elliptic, with a 
period of nearly 2000 years. In 1861 appeared another great comet. 
Its tail was fan-shaped, with six distinct emanations, all perfectly 
straight. The outer ones attained the enormous apparent length of 
nearly 120°, and were very divergent, owing to immersion of the earth 

in the material of the tail to a 
depth of 300.000 miles. This comet 
also travels round the sun in an 
elliptic path, with a period exceed- 
ing 400 years. The next fine comet 
appeared in 1874, and is known as 
Coggia's comet. Its nucleus was 
of the first magnitude, and its tail 
50° in length, and very slightly 
curved. Coggia's comet was the 
first of striking brilliancy to which 
the spectroscope was applied, and 
it was found that its gaseous sur- 
roundings were in large part com- 
posed of hydrogen compounded 
with carbon. Coggia's comet, when 
far from perihelion, presented an 
anomalous appearance, well shown 
in the opposite illustration — a 
bright streak immediately following 
the nucleus and running through the middle of the tail. When nearer 
the sun, this streak was replaced by the usual dark one. No sufficient 
explanation of either has yet been proposed. The orbit of Coggia's 
comet is an ellipse of so great eccentricity that this body cannot 
reappear for thousands of years. 

Remarkable Comets between 1875 and 1890. — Only two require 
especial mention, the first of which was discovered in 1881, and was a 
splendid object in the northern heavens in June of that year. It was 
similar in type to Donati's comet of 1858, and was the first comet ever 
successfully photographed. In 1882 there were two bright comets, one 
of them in many respects extraordinary. So great was the intrinsic 
brightness that it was observed with the naked eye, close alongside 
the sun. Indeed, it passed between the earth and the sun, in actual 
transit ; and just before entering upon the disk, the intrinsic brightness 
of the nucleus was seen to be scarcely inferior to that of the sun itself. 
It was a comet of huge proportions. Its tail stretched through space 
over a distance exceeding that of the sun from the earth, and parts of 




Donati's Triple-tailed Comet of 1858 



When Will the Next Comet Come 



405 



its head passed within 300,000 miles of the solar surface, at a speed 
of 200 miles a second. Probably this near approach explains what was 
seen to take place on recession from the sun — the breaking up of the 
comet's head into several separate nuclear masses, each pursuing an 
independent path. Also this comet's tail presented a variety of unusual 
phenomena, at one time being single and nearly straight, while again 
there were two tails slightly curved. 
Besides this, its coma was sur- 
rounded by an enormous sheath or 
envelope several million miles long, 
extending toward the sun. 

Remarkable Comets since 1890. — 
No very bright comet appeared 
between 1882 and 1897; but the 
Brooks comet of 1893, although a 
faint one and at no time visible to 
the naked eye, is worthy of note 
because of some remarkable photo- 
graphs of it obtained by Barnard. 
The illustration (next page) is re- 
produced from one of them, and 
enlarged from the original negative. 
Changes in this comet were rapid 
and violent, and the tail appeared 
broken and distorted, like * a torch 
flickering and streaming irregularly 
in the wind.' Ejections of matter from the comet" s nucleus may have 
been irregular or it may have encountered some obstacle which shat- 
tered it — perhaps a swarm of meteors. 

When will the Next Comet come ? — If a large bright 
comet is meant, the answer must be that astronomers 
cannot tell. One may blaze into view at almost any time. 
During the latter half of the 19th century, bright comets 
have come to perihelion at an average interval of about 
seven years. But already (1897) this interval has been more 
than doubled since the last great comet (1882). A bright 
one is certain, however, in 1910, because Halley's periodic 
comet, last seen in 1835, will return in that year. Of the 
lesser and fainter periodic comets, several return nearly 
every year ; but they are for the most part telescopic, and 




Drawings of Coggia's Comet U874) 



4o6 



Comets a7id Meteors 



rarely attract the attention of any one save the astronomers. 
Three are due in 1898, and five in 1899. 

Light of Comets. — The Hght of comets is dull and feeble, 
and not always uniform. When in the farther part of 
their orbits, comets seem to shine only 
by light reflected from the sun ; and 
that is why they so soon become invis- 
ible, on going aw^ay from perihelion. 
They are then bodies essentially dark 
and opaque. But with approach to- 
ward the sun, the vast increase in bright- 
ness, often irregular, is due to light 
emitted by the comet itself, and it is 
this intrinsic brightness of comets, 
that, for the most part, makes them 
the striking objects they are. In some 
manner not completely understood, radia- 
tions of the sun act upon loosely com- 
pacted materials of the comet's head, 
producing a luminous condition which, 
in connection with the repulsive force 
exerted by that central orb gives rise to 
all the curious phenomena of the heads 
and tails of comets. 

Chemical Composition. — Through 
analysis of the light of comets by the 
spectroscope, it is known that the chief 
element in their composition is carbon, 
combined with hydrogen ; that is, hydro- 
carbons. The elements so far found are 
few. Sodium, magnesium, and iron were 
found in the great comet of 1882; also nitrogen, and 
probably oxygen. It is not certain that the spectrum of 
a comet remains always the same; perhaps there are 




Brooks's Comet of 

1893 (photographed 

by Barnard) 



Comets Discovered during Eclipses 407 

rapid changes on approaching the sun. The faint contin- 
uous spectrum, a background for brighter lines in the blue, 
green, and yellow, is reflected sunlight. 

The illustration shows a part of the spectrum of the comet of 1882, 
with the Fraunhofer lines G,h,H,K, and others, whose presence dis- 
tinctly confirms this hypothesis. The spectra of between 20 and 30 
comets have been observed in all, and they appear to have in general 
very nearly the same chemical composition. 




37 38 39 40 41 42 43 44 45 46 47 




illHIili 

Spectrum of Comet of 1882 (Sir William Huggins"* 

Photographing Comets. — The light of a comet is usually feeble, at 
least so far as the eye is concerned,, and its actinic power is even less. 
How then can a comet be photographed? Evidently in one of two 
ways only. Either the photographic plate must be very sensitive, or 
the exposure must be very long. Before invention of the modern 
sensitive dry plate, it had been found impossible to photograph comets. 
The first photograph of a comet w^as made by Henry Draper, who 
photographed the comet of 1880. Since 1890 many faint comets have 
been successfully photographed at the Lick Observatory, and elsewhere, 
by the use of very sensitive plates and a long exposure. Next illus- 
tration shows a photograph of Gale's comet (1894), in which the expo- 
sure was prolonged to i h. o m. The comet was moving rapidly, and 
as the clockwork moving the telescope was made to follow the comet 
accurately, all stars adjacent to it appear upon the photograph, not as 
points of light, but as parallel trails of equal length. Husseyand Wil- 
son have met with equal success. 

Comets discovered during Eclipses. — Probably more 
than one half of all comets coming within range of 
visibility from earth remain undiscovered, because of the 
overpowering brilliancy of the sun. Ought not, then, new 
comets to be discovered during total eclipses of the sun ? 
This has actually happened on at least tw^o such occasions, 
and a like appearance has been suspected on two more. 



4o8 



Comets and Meteors 



During the total eclipse of the 17th of May, 1882, observed in Egypt, 
Schuster photographed a new comet alongside the solar corona, as 
shown on page 301. This comet was named for Tewfik, who was then 
khedivx. Also another comet was similarly photographed, but joining 
immediately upon the streamers of the corona, during 
the total eclipse of the i6th of April, 1893, by Schaeberle 
in Chile. Both of these comets were new discoveries, 
and neither of them has since been seen. As there is 
but one observation of each, nothing is known about 
their orbits round the sun, nor w^hether they will ever 
return. 

Mass and Density, — So small are the masses 
of comets that only estimates can be given as 
compared with the mass of the earth. Comets 
have in certain instances approached very near 
to lesser bodies of the solar system ; but while 
cometary orbits and motions have been greatly 
disturbed thereby, no change has been ob- 
served in the motion of satellites or other 
bodies near which a comet has passed. So 
this mass must be slight. Probably no comet's 
mass is so great as the yo"^o"o" P^^^ ^^ ^^^ 
earth's; but even if only one third of this, it 
would still equal a ball of iron 100 miles in 
diameter. If the mass of comets is so small, 
while their volume is so vast, what must be 
the density of these bodies } For the density 
is equal to the mass divided by the volume, 
and comets must, therefore, be exceedingly 
thin and tenuous. On those rare occasions 
when stars have been observed through the 
tail of a comet, although it may be millions 
of miles in thickness, still no diminution of the star's 
luster has been perceived. Even through the denser coma 
the light of a star passes undimmed ; though the star's 
image, if very near the comet's nucleus, may be rendered 



Gale's Comet 

of 1894 

(photographed 

by Barnard) 



Collision zvith a Comet 409 

somewhat indistinct. The air pump is often used to pro- 
duce an approach to a perfect vacuum ; but in a cubic 
yard of such vacuum there would be many hundred times 
the amount of matter in a cubic yard of a comet's head. 

Passing through a Comet's Tail. — Curious as it may 
seem, these enormous tails are in actual mass so slight 
that thrusting the hand into their midst would bring no 
recognition to the sense of touch. Collision would be 
much like an encounter with a shadow. Comets' tails 
are excessively airy and thin, or, as Sir John Herschel 
remarks, possibly only an affair of pounds or even ounces. 

The mass of a comet's head may be large or small ; it may not be 
more than a very large stone, or in the case of the larger comets it is 
perfectly possible that the mass of the head should be composed of an 
aggregation of many hundreds or even thousands of small compact 



Earth about to pass through Tail of Comet of 1861 

bodies, stony and metallic. Usually the speed is so great that the 
comet itself would be dissipated into vapor on experiencing the shock 
of collision with any of the planets. In at least two instances it is 
known that the earth actually passed through the tail of a comet, once 
on 30th June, 1861. The figure shows positions of sun (S)^ head of 
comet (^), and earth (/), just before our planet's plunge into the diaph- 
anous tail. But we came through without being in the least con- 
scious of it, except from calculations of the comet's position. 

Collision with a Comet. — As the orbits of comets lie at all 
possible inclinations to the earth's path, or ecliptic, and as 
the motion of these erratic bodies may be either direct or 
retrograde, evidently it is entirely possible that our planet 
may some time collide with a comet, because these bodies 



4IO Comets and Meteors 

exist in space in vast numbers. It has been estimated 
that one such colHsion must take place every 15,000,000 
years, so that the chances are immensely against the hap- 
pening of such an event at any specified time, and comets 
can hardly be regarded as dangerous bodies. Not only 
would it be futile, but not worth the while to ' excommuni- 
cate ' them, as the pope did in centuries gone by. 

However, should the head of a large comet collide squarely with our 
globe — the consequences might be inconceivably dire: probably the 
air and water would be instantly consumed and dissipated, and a con- 
siderable region of the earth^s surface would be raised to incandescence. 
But consequences equally malign to human interests might result from 
the much more probable encounter of the earth's atmosphere with 
solid particles of a large hydrocarbon comet : it might well happen that 
diffusion of noxious gases from sudden combustion of these compounds 
would so vitiate the atmosphere as to render it unsuitable for breathing. 
In this manner, while the earth itself, its oceans, and even human habi- 
tations, might escape unharmed, it is not difficult to see how even a 
brush from the head of a large comet might cause universal death to 
nearly all forms of animal existence. 

Origin of Comets. — The origin of comets is still shrouded in mys- 
tery. Probably they have come from depths of the sidereal universe, 
and so are entirely extra-solar in origin. Arriving apparently from 
all points of space in their journey from one star to another, they 
wheel about the sun somewhat like moths round a candle. Sometimes, 
as already shown, they speed away in a vast ellipse, with the promise 
of a future visit, though at some date which cannot be accurately 
assigned. Sometimes they continue upon interstellar journeys of such 
vast parabolic dimensions, perhaps round other suns, that no return 
can ever be expected. Probably the comets are but chips in the work- 
shop of the skies, mere waste pieces of the stuff that stars are made of. 
It has been urged, too, that some comets may have originated in vapor- 
ous materials ejected by our own sun, or the larger planets of our 
system ; but here we tread only the vast fields of mere conjecture, 
tempting, though unsatisfying. 

Disintegration of Comets. — Every return to perihelion 
appears to have a disintegrating effect upon a comet. 
In a few cases this process has actually been taking 
place while under observation ; for example, the lost 



Meteors and Shooting Stars 411 

Biela's comet in 1846, the great comet of 1882, and 
Brooks's comet of 1889, the heads of which were seen 
either to divide or to be divided into fragments. Groups 
of comets probably represent a more complete disinte- 
gration. 

For example, the comets of 1843, 1880, 1882, and 1887 travel tandem, 
and originally were probably one huge comet. In the case of still other 
comets, this disintegration has gone so far that the original cometary 
mass is now entirely obliterated. Instead of a comet, then, there 
exists only a cloud of very small fragments of cometary matter, too 
small, in fact, to be separately visible in space. Such interplanetary 
masses, originally single comets of large proportions, have by their 
repeated returns to the sun been completely shattered by the oft- 
renewed action of disrupting forces ; and all that is now left of them is 
an infinity of meteoric particles, trailing everywhere along the original 
orbit. The astronomer becomes aware of the existence of these small 
bodies only when they collide with our atmosphere, sometimes pene- 
trating even to the surface of the earth itself. 

Meteors, Shooting Stars, and Meteorites. — Particles of 
matter thought to have their origin in disintegrated comets, 
and moving round the sun in orbits of their own, are 
called meteors. In large part, our knowledge of these 
bodies is confined to the relatively few which collide with 
the earth. The energy of their motion is suddenly con- 
verted into heat on impact with the atmosphere, and fric- 
tion in passing swiftly through it. As a rule, this speedily 
vaporizes their entire substance, the exterior being brushed 
off by the air as soon as melted, often leaving a visible train 
in the sky. The luminous tracks pass through the upper 
atmosphere, few if any meteors appearing at greater 
heights than 100 miles, and few below 30 miles. These 
paths, if very bright, can be recorded with great precision 
by photography as Wolf, Barnard, and Elkin have done. 
As the speed of meteors through the air is comparable with 
that of our globe round the sun, we know that their motion 
is controlled by the sun's attraction, not the earth's. 



412 Comets aizd Meteors 

Very small meteors, sometimes falling in showers, are frequently 
called shooti/ig stars, but the late Professor Newton's view is gradually 
gaining ground, that there is no definite line of distinction. The 
shooting stars are thought to be very much smaller than meteors, 
because they are visible for only a second or two, and disappear 
completely at much greater heights than the meteors do. Many 
millions of them collide with our atmosphere every day, and are 
quickly dissipated. Although the average of them are not more mas- 
sive than ordinary shot, their velocity is so great that all organic beings, 
without the kindly mantle of the air (were it possible for such to live 
without it) would be pelted to death. If a meteor passes completely 
through the atmosphere, and reaches the surface of the earth, it be- 
comes known as a meteorite. Many thousand pounds of such inter- 
planetary material have been collected from all parts of the earth, 
and the specimens are jealously preserved in cabinets and museums, 
the most complete of which are in London, Paris, and Vienna. Re- 
markable collections in the United States are at Amherst College, 
Harvard and Yale Universities, and in the National Museum at 
Washington. 

Meteors most Abundant in the Morning. — Run rapidly in a rain- 
storm : the chest becomes wetter than the back, because of advance 
of the body to meet the drops. In like manner, the forward or advance 
hemisphere of the earth, in its motion round the sun, is pelted by more 
meteors than any other portion. As every part of the earth is turned 
toward the radiant during the day of 24 hours, it is obvious that 
the most meteors will be counted at that hour of the day when the 
dome of the sky is nearly central around the general direction of our 
motion about the sun ; in other words, when apex of earth's way is 

nearest to the zenith. Recall- 
ing the figures on pages 134- 
5, it is apparent that this takes 
place about sunrise ; and in 
the adjacent illustration, 
where the sun is above the 
earth, and illuminating the 
hemisphere abd, it is sunrise 
When Meteors are most Abundant ^^ d, and the earth is speed- 

ing through space in the di- 
rection dp, indicated by the great arrow. So the hemisphere adc is 
advancing to meet the meteors which seem to fall from the directions 
ggg. If we suppose meteoric particles evenly distributed throughout 
the shoal, the number becoming visible by collision with our atmos- 
phere will increase from midnight onward to six in the morning, pro- 
vided the season is such that dawn does not interfere. From noon at 




The Radiant Point 



413 



a to sunset at b. there would be a gradual decrease, with the fewest 
meteors falling from the directions fff^ upon the earth^s rearward 
hemisphere, abc. Also, as to time of the year, it is well known that our 
globe encounters about three times as many shooting stars in passing 
from aphelion to periheUon as from perihelion to aphelion. 



Radiant Point. — On almost any clear, moonless night, 
especially in April, August, November, and December, a 
few moments of close watching will show one or more 
shooting stars. Ordinarily, they appear in any quarter of 
the sky ; and on infrequent occasions they streak the 
heavens by hundreds and thousands, for hours at a time, 
as in November of 1799 and 1833. These are known as 
meteoric showers. Careful watching has revealed the very 
important fact, that practically all the luminous streaks of 
a shower, if prolonged backward, meet in a small area 
of the sky which is fixed among the stars. Arrows in the 
following figure represent the visible paths of 20 meteors, 
and the direction of their flight. It is clear that lines drawn 
through them will nearly all 
strike within the ring. This 
area is technically known as 
the radiant point, or simply 
the radiant. Divergence 
from it in every direction is 
only apparent — a mere effect 
of perspective, proving that 
meteors move through space 
in parallel lines. The radiant 
is simply the vanishing point. 
Notice that the luminous 
paths are longer, the farther they are from the radiant ; if 
a meteor were to meet the earth head on, its trail would 
be foreshortened to a point, and charted within the area of 
the radiant itself. About 300 such radiant points are now 




To Illustrate the Radiant Point 



414 



Comets and Meteors 



known, of which perhaps 50 are very well established. 
The constellation in which the radiant falls gives the 
name to the shower ; so there are Leonids and Perseids, 
Andromedes and Geminids, and the like. 

List of Principal Meteor Showers. — Following is given, in tabular 
form, a short list of the chief meteoric displays of the year, according to 
Denning, a prominent English authority : — 

Annual Showers of Meteors 







Position of Radiant 


Date of . 

Maximum 


Duration in 




R A. 


Decl. 


Days 


Quadrantids . 
Lyrids . . . 
Eta Aquarids 
Delta Aquarids 
Perseids . . 
Orionids . . 
Leonids . . 
Andromedes 
Geminids . . 




I5h. 19m. 

17 59 
22 30 
22 38 

3 4 

6 8 
10 

I 41 

7 12 


N. 53^ 
N. 32 
S. 2 

S. 12 

N.57 

N. 15 
N. 23 
N. 43 
N. 33 


Jan. 2 
April 18 
May 2 
July 28 
Aug. 10 
Oct. 19 
Nov. 13 
Nov. 26 
Dec. 7 


2 

4 
8 

3 
35 
10 

2 

2 

14 



When more than one radiant falls in any constellation, the usual 
designation of the nearest star is added, to distinguish between them. 

Paths of Meteors. — Repeated observation of the paths 
of meteors belonging to any particular radiant soon estab- 
lishes the fact that showers recur at about the same time 
of the year. Also in a few instances the shower is very 
prominently marked at intervals of a number of years. 
So it has become possible to predict showers of meteors, 
which on several occasions have been signally verified. 
Conspicuously so is the case of the shower of November, 
1866, which came true to time and place; and a like 



Meteoric Orbits 



415 



shower is confidently predicted for 12th- 14th, November, 
1899. The periodic time of these meteors is 33^ years. 

The position of their radiant among the stars, and the direction in 
which the meteors are seen to travel, has afforded the means of calcula- 
ting the size and shape of their orbit, and just where it lies in space. 
The figure shows the orbit of the Leonids, or November meteors, as 
related to the paths of the planets, and it is evident that these bodies, 
although they pass at a distance 
of 100,000,000 miles from the 
sun at their perihelion, recede 
about i6| years later to a dis- 
tance greater than that of Ura- 
nus. They are not aggregated 
at a single point in their orbit, 
but are scattered along a con- 
siderable part of it, called the 
^ Gem of the ring."* As the 
breadth of the gem takes more 
than two years to pass the peri- 
helion point, which nearly coin- 
cides with the position of the 
earth in the middle of Novem- 
ber, there will usually be two or 
three meteoric showers at yearly 
intervals, while the entire shoal 
is passing perihelion. So that 
lesser showers may be expected 
in November of 1898 and 1900, 
in addition to the chief shower 
of 1899. 

Meteoric Orbits in Space. 

— But it must not be in- 
ferred from the figure here 
given that the Leonids 
travel in the plane of the 

planetary orbits ; for, at the time when their distance 
from the sun is equal to that of the planetary bodies, 
they are really very remote from all the planets except 
the earth and Uranus. This is because of the large angle 




Orbit of Comet I (1866) and of the Novem- 
ber Meteors 



4i6 



Comets and Meteors 



of 17° by which the orbit of the November meteors 
is inclined to the ecHptic. It stands in space as the ad- 




Perihelion Parts of Orbits of the August and November Meteor- showers 

jacent figure shows, being the lower one of the two orbits 
whose planes are cut off. Similarly, the upper and nearly 
vertical plane represents the position in space of another 
meteoric orbit, which intersects our path about loth 
August. This shower is therefore known as the August 
shower ; also these meteors are often called Perseids. 



What are Meteo7'S 417 

As shown by the arrows, both the Perseicls and the Leonids travel 
oppositely to the planets ; so that their velocity of impact with our 
atmosphere is compounded of their own velocity and the earth's also. 
This average speed for the Leonids, about 45 miles per second, is 
great enough to vaporize all meteoric masses within a few seconds ; 
so it is unlikely that a meteoric product from the Leonids will ever be 
discovered. Impact velocity of the Andromedes is very much less, 
because they overtake the earth. In the case of meteorites, the velocity 
of ground impact probably never exceeds a few hundred feet per second. 
so great is the resistance of the air : and several meteoric stones which 
fell in Sweden, ist January. 1869. on ice a few inches thick, rebounded 
without either breaking it or being themselves broken. 

Connection between Comets and Meteors. — Xot long 
after the important discovery of the motion of meteors in 
regular orbits, an even more significant relation was as- 
certained : that the orbits of the Perseids and the Leonids 
are practically identical with the paths in which two comets 
are known to travel. The orbit of the Leonids is coinci- 
dent with that of Tempel's comet (1866 i), and the Perseids 
pursue the same track in space with Swift's comet (known 
as 1862 III). The latter, has a period of about 120 years, 
and recedes far beyond the planet Xeptune. So do the 
meteors traveling in the same track. They are much 
more evenly distributed all along their path than the 
Leonids are ; and no' August ever fails of a slight sprinkle, 
although the shorter nights in our hemisphere often inter- 
fere with the display. 

What are Meteors ? — Several other meteor swarms and 
comets have been investigated with a like result ; so the 
conclusion is now well established that these meteors, and 
probably all bodies of that nature, are merelv the shattered 
residue of former comets. This important theory is con- 
firmed, whether we look backward in the life of a comet, 
or forward : if backward, comets are known to disintegrate, 
and have indeed been • caught in the act ' ; if forward, our 
expectation to find the disruption farther advanced in the 
todd's astron. — 27 



41 8 Comets and Meteors 

case of some comets and meteors than others is precisely 
confirmed by the facts regarding different showers. Then, 
too, as will be shown in a later paragraph, the spectra 
of meteorites vaporized and photographed in our lab- 
oratories are practically identical with the spectra of the 
nuclei of comets. The conclusion is, therefore, that these 
latter are nothing more than a compact swarm or shoal 
of meteoric particles, vaporized in their passage through 
space, under conditions not yet fully understood. The 
practical identity of composition between comets and 
meteors had long been suspected, but it was not com- 
pletely confirmed until 27th November, 1885, when mete- 
orites which fell to the earth from a shower of Bielids were 
picked up in Mexico, and chemical and physical investiga- 
tion established their undoubted nature as originally part 
of the lost Biela's comet. 

Falls of Meteorites. — In general the meteorites are 
divided into two classes : meteoric stones and meteoric 
irons. Falls of the stony meteorites have been much 
oftener seen than actual descents of masses of meteoric 
iron. The most remarkable fall ever seen took place on 
loth May, 1879, in Iowa, the heaviest stone weighing 437 
pounds. This is two thirds the weight of the largest 
meteoric stone ever discovered, though not actually seen 
to fall. It was found in Hungary in 1866, and is now part 
of the Vienna collection. The iron masses are often much 
heavier: the ^signet' meteorite, a complete ring found in 
Tucson, Arizona, and now in the United States National 
Museum at Washington, weighs 1400 pounds; a Texas 
meteorite, now part of the Yale collection, weighs 1635 
pounds ; and a Colorado meteorite in the Amherst collec- 
tion weighs 437 pounds. But although the cabinets con- 
tain hundreds of specimens of meteoric irons, only eight or 
ten have actually been seen to fall. 



Analysis of Meteorites 



419 



Of these, the largest one fell in Arabia in 1865, and its weight is 130 
pounds. It is now in the British Museum. The average velocity of 
meteors is 35 miles per second. Their visibility begins at an altitude 
of about 70 miles, and they fade out at half that height. The work 
done by the atmosphere in suddenly checking their velocity appears in 
large part as heat which fuses the exterior to incandescence, and leaves 
them, when cooled, thinly encrusted as if with a dense black varnish. 
The iron meteorites, not reduced by rust, are invariably covered with 
deep pittings or thumb marks. Meteorites are always irregular in form, 
never spherical ; and the pittings are in part due to impact of minute 
aerial columns which resist their swift passage through the air. 

Analysis of the Meteorites. — Meteoric iron is an alloy, 
containing on the average ten per cent of nickel, com- 
mingled with a much smaller amount 
of cobalt, copper, tin, carbon, and a 
few other elements. Meteoric iron 
is distinguishable from terrestrial 
irons by means of the 'Widmann- 
stattian figures,' which etch them- 
selves with acids upon the polished 
metallic surface — a test which rarely 
fails. The illustration shows these 
figures of their true size, as it was 
made from a transfer print from the 
actual etched surface of a meteorite 
in the Amherst collection. In me- 
teoric stones, chemical analysis has revealed the pres- 
ence of about one third of all the elemental substances 
recognized in the earth's crust ; among them the elements 
found in meteoric irons, also sulphur, calcium, chlorine, 
sodium, and many others. 

The minerals found in meteoric stones are those which abound in 
terrestrial rocks of igneous or volcanic origin, like traps and lavas. 
Carbon sometimes is found in meteorites as diamond. The analysis 
of meteorites has brought to light a few compounds new to mineralogy, 
but has not yet led to the discovery of any new element : and the study 




Widmannstattian Figures 



420 Comets and Meteors 

of meteorites is now the province of the crystallographer, the chemist, 
and the mineralogist, rather than the astronomer. Even the most 
searching investigation has so far failed to detect any trace of organic 
life in meteorites. 

Occlusion is the well-known property of a metal, par- 
ticularly iron, by which at high temperatures it absorbs 
gases, and retains them until again heated red hot. Hy- 
drogen, carbonic oxide, and nitrogen are usually present in 
iron meteorites as occluded gases, also, in very small quan- 
tities, the light gas, newly discovered, called helium. In 
1867, during a lecture on meteors by Graham, a room 
in the Royal Institution, London, was lighted by gas 
brought to earth in a meteorite from interplanetary space. 
We have now traversed the round of the solar system ; it 
remains only to consider the bodies of the sidereal system, 
and the views held by philosophers concerning the pro- 
gressive development of the material universe. 



CHAPTER XVI 

THE STARS AND THE COS^IOGOXY 

OUR descriptions of heavenly bodies thus far have con- 
cerned chiefly those belonging to the solar system. 
We found distance growing vast beyond the power 
of human conception, as we contem.plated, first the neigh- 
borly moon, then the central orb of the system 400 times 
farther away, and finally Xeptune, 30 times farther than 
the sun, — not to say some of the comets whose paths 
take them even remoter still. But outside of the solar 
system, and everywhere surrounding it, is a stellar universe 
the number of Avhose countless hosts is in some sense a 
measure of their inconceivable distance from our humble 
abode in space. 

The Sidereal System. — All these bodies constitute the 
sidereal system, or the stellar universe. It comprises stars 
and nebulae ; not only those which are visible to the naked 
eye, but hundreds of thousands besides, so faint that their 
existence is revealed only by the greatest telescopes and 
the most sensitive photographic plates. Remoteness of 
the stars at once forbids supposition that they are similar 
in constitution to planets, shining by light reflected from 
the sun as the moon and planets do. Even Xeptune, on the 
barriers of our system, is too faint for the naked eye to 
grasp his light. But the nearest fixed star is about 9000 
times more distant. So the very brightness of the lucid 
stars leads us to suspect that they at least must be self- 
luminous like the sun ; and when their lio-ht is analvzed 

421 



4^2 



Stars and Cosmogony 



with the spectroscope, the theory that they are suns is 
actually demonstrated. It is reasonable to conclude, then, 
that the sun himself is really a star, whose effulgence, and 
importance to us dwellers on the earth, are due merely to 
his proximity. The figure below will help this conception : 
for if we recede from the sun even as far as Neptune, his 
disk will have shrunk almost to a point, though a dazzling 
one. Were this journey to be continued to the nearest 
star, our sun would have dwindled to the insignificance 
of an ordinary star. 

The Magnitudes of Stars. — While stars as faint as the 
sixth magnitude can just be seen by the ordinary eye on 

a clear dark night, still 
other and fainter stars can 
be followed with the tele- 
scope far beyond this 
limit, to the fifteenth mag- 
nitude and even farther 
by the largest instruments. 
Division into magnitudes, 
although made arbitrarily, 
is a classification war- 
ranted by time, and use 
of many generations of 
astronomers. Brightness 
of stars decreases in geo- 
metric proportion as the 
number indicating magni- 
tude increases ; the con- 
stant term being 2\. Thus, 
an average star of the first magnitude is 2\ times brighter 
than one of the second magnitude; a second magnitude 
star gives 2\ times more light than one of the third magni- 
tude, and so on. At the observatory of Harvard College, 




Our Sun but a Brilliant Star as seen from 
Neptune 



The Brightest Stars 



423 



Pickering, its director, has devoted many years to determi- 
nation of stellar magnitudes with the meridian photometer, 
a highly accurate instrument of his devising, by which 
the brightness of any star at culmination may be compared 
directly with Polaris as a standard. Brightest of all the 
stars is Sirius, and as no others are so brilliant, strictly 
he ought perhaps to be the only first magnitude star. But 
many fainter than Sirius are ranked in this class, three 
of them so bright that their stellar magnitude is negative, 
as below. Decimal fractions express all gradations of 
magnitude. Even the surpassing brilliancy of the sun 
can be indicated on the same scale; the number— 25.4 
expresses his stellar magnitude. 

The Brightest Stars. — Twenty stars are rated of the 
first magnitude ; half of them are in the northern hemi- 
sphere of the sky. They are the following : — 

The Brightest Stars 



Order 

OF 

Bright- 
ness 


Stellar 
Mag- 
nitude 


Stars' Names 


Order 

OF 

Bright- 
ness 


Stellar 
Mag- 
nitude 


Stars' Names 


I 


-1.4 


a Canis Majoris {Sirius) 


II 


0.9 


aOrionis {Betelgeux) 


2 


-0.8 


a Argus {Canopies)* 


12 


0.9 


0. Crucis * 


3 


—0.1 


a. Centauri* 


13 


0.9 


aAquilas {Altair) 


4 


0.1 


a Aurigae ( Cap ell a) 


14 


I.O 


a- Tauri {Aldebara?z) 


5 


0.2 


a Bootis {Arcturus) 


15 


I.I 


aVirginis {Spied) 


6 


0.2 


a Lyrag ( Vega) 


16 


1.2 


a Scorpii {Antares) 


7 


0-3 


/3 Ononis {Rigel) 


17 


1.2 


/3 Geminorum {Pollux) 


8 


0.4 


a. Eridani {Achernar) * 


18 


1-3 


a Piscis Australis 


9 


0-5 


a Canis Minoris 






{Fonialhaut) 






{Procyon) 


19 


1-3 


a Leon is {Regulus) 


10 


0.7 


iS Centauri * 


20 


14 


a Cygni {Deueb) 



These stars culminate at different altitudes varying 
with their declination, and at different times throuo^hout 



* Invisible in our middle northern latitudes, 



424 Stars and Cosmogony 

the year, which you may find from charts of the constella- 
tions (pp. 60-63). 

Number of the Stars. — Besides twenty stars of the first 
magnitude, not only are there nearly six thousand of 
lesser magnitude visible to the naked eye, likewise many 
hundreds of thousands visible in telescopes of medium 
size, but also millions of stars revealed by the largest 
telescopes. From careful counts, partly by Gould, the 
number of stars of successive magnitudes is found to in- 
crease nearly in geometric proportion : — 



1st magnitude 20 


6th 


magni 


tude 


5000 


2d '• 65 


7th 


u 




20,000 


3d " 200 


8th 


u 




68,000 


4th " 500 


9th 


ii. 




240,000 


5th - " 1400 


loth 


a 




720,000 



Any glass of two inches aperture should show all these 
stars. But in order to discern all the uncounted millions 
of yet fainter stars, we need the largest instruments, like 
the Lick and the Yerkes telescopes. Their approximate 
number has been ascertained not by actual count, but 
by estimates based on counts of typical areas scattered 
in different parts of the heavens. The number of stars 
within reach of our present telescopes perhaps exceeds 
125 millions. But the telescope by itself, no matter 
how powerful, is unable to detect any important difference 
between these faint and multitudinous luminaries ; seem- 
ingly all are more alike than peas or rice grains to the 
naked eye. There is good reason for believing that the 
dark or non-luminous stars are many times more numerous 
than the visible ones, and modern research has made the 
existence of many such mvisible bodies certain. 

Total Light from the Stars. — Argelander, a distin- 
guished German astronomer, made a catalogue and chart 
of all the stars of the northern hemisphere increased by 



Colors of the Stars 425 

an equatorial belt, one degree in width, of the southern 
stars. His limit was the 9^ magnitude, and he recorded 
rather more than 324,000 stars in all. Accepting a sixth 
magnitude star as the standard, and expressing in terms of 
it the light of all the lucid stars registered by Argelander, 
they give an amount of light equivalent to 7300 sixth 
magnitude stars. But calculation proves also that the 
telescopic stars of this extensive catalogue yield more than 
three times as much light as the lucid ones do. The stars, 
then, w^e cannot see with the naked eye give more light 
than those we can, because of their vastly greater num- 
bers. If, now, we suppose the southern heavens to be 
studded just as thickly as the northern, there would be in 
the entire sidereal heavens about 600,000 stars to the 
9| magnitude ; and their total light has been calculated 
equal to -^-^ that of the average full moon. 

Colors of the Stars. — A marked difiference in color characterizes 
many of the stars. For example, the polestar and Procyon are white, 
Betelgeux and Antares red, Capella and Alpha Ceti yellowish, Vega 
and Sirius blue. Among the telescopic stars are many of a deep blood- 
red hue; variable stars are numerous among these. In observing true 
stellar colors, the objects should be high above the horizon, for the 
greater thickness of atmosphere at low altitudes absorbs abundantly the 
bluish rays, and tends to give all stars more of an orange tint than they 
really possess. Colors are easier to detect in the case of double stars 
(page 451), because the components of many of these objects exhibit 
complementary colors ; that is, colors w^hich produce white light when 
combined. If components of a ' double^ are of about the same magni- 
tude, their color is usually the same : if the companion is much fainter, 
its color is often of complementary tint, and ahvays nearer the blue end 
of the spectrum. Complementary colors are better seen with the stars 
out of focus. Following are a few of these colored double stars : — 

77 Cassiopeiae. yellow and purple. 
y Andromedae. orange and green, 
I Cancri, orange and blue, 

a Herculis, orange and green, 
^ Cygni, yellow and blue, 



4 rnag. 


1\ mag. 


3^T 


5^ 


4i 


6 


3 


6 


3 


7 



426 Stars and Cosmogony 

There is some evidence that a few stars vary in color in long periods 
of time ; for example, two thousand years ago Sirius was a red star, 
now it is bluish white. Any significance of color as to age or intensity 
of heat is not yet recognized ; rather is it probably due to variant com- 
position of stellar atmospheres. 



Star Catalogues and Charts. — When you consult a 
gazetteer you find a multitude of cities set down by name. 
Corresponding to each is its latitude, or distance from 
the equator, and its longitude, or arc distance on the 
equator, measured from a departure point or prime merid- 
ian. These arcs are measured on the surface of our 
earth. Turning, then, to the map, you find the city in 
question, and perhaps many neighboring ones set down in 
exact relation to it. Precisely in a similar manner all the 
brighter stars of the sky are registered in their true rela- 
tions one to another, on charts and photographic plates. 
These will be accurate enough for many purposes, but not 
for all. When a higher precision is required, one must 
consult those gazetteers of the sky known as star cata- 
logues. Set down in them will be found the coordinates 
of a star ; that is, its right ascension and declination, the 
counterparts of terrestrial longitude and latitude. But we 
shall soon observe this peculiar difference between longitude 
on the earth and right ascension in the sky : the star's right 
ascension will (in nearly all cases) be perpetually increas- 
ing, while the longitude of a place remains ahvays the 
same. This perpetual shifting of the stars in right ascen- 
sion is mostly due to precession. It is as if Greenwich or 
Washington were constantly traveling westward, but so 
slowly that only in 26,000 years would it have traveled all 
the way round the globe. 

Precession and Standard Catalogues. — It was Hipparchus 
(b.c. 130) who first discovered this perpetual and apparent 
shifting of all the stars. And partly for this reason he 



Photographic Charts of the Heavens 427 

made a catalogue (the first one ever constructed) of 1080 
stars, so that the astronomers coming after him might, by 
comparing his map and catalogue with their own, dis- 
cover what changes, if any, are in progress among the 
stellar hosts. No competitor appeared in the field, until 
the 15th century, when the second catalogue w^as con- 
structed, by Ulugh-Beg (a.d. 1420), an Arabian astrono- 
mer. Since his day vast improvements have been made 
in methods of observing the stars, and in calculating 
observations of them. There are now about 100 large 
catalogues of stars, constructed by astronomers of both 
hemispheres ; and the place of every star in the entire 
celestial sphere revealed by telescopes of medium dimen- 
sion will soon be determined with astronomical precision. 
Several of the larger government observatories prepare a 
catalogue of stars every year from their observations ; and 
these again are combined into other and more accurate 
catalogues (called standard catalogues), especially of the 
zodiacal stars. These afford average or mean positions of 
stars for the beginning of a particular year, called the 
epoch of the catalogue. Positions for any given dates are 
obtained by bringing the epoch forward, and farther cor- 
recting for precession, aberration, and nutation (pages 130, 
164, and 390). The mean position so corrected becomes 
the apparent place. The chief American authorities on 
standard stellar positions are Newcomb, Boss, and Safford. 

Photographic Charts of the Entire Heavens. — On proposal of David 
Gill, her Majesty's astronomer at the Cape of Good Hope, an inter- 
national congress of astronomers met at Paris in 1887. and arranged for 
the construction of a photographic chart of the entire heavens. The 
work of making the charts has been allotted to 18 observatories, one 
third of which are located in the southern hemisphere. They are 
equipped with 13-inch telescopes, all essentially alike: and exposures 
are of such length as to include all stars to the 14th magnitude, prob- 
ably more than 50 millions in all. Stars to the i ith magnitude inclusive 
(about 2,000,000) are to be counted and their positions measured and 























m 


















.'•^ 










* ^ 






i '« 


♦ * 










■ 1 






% 




" * > ' 




*■* 




' f 




* . 


»"■ 




* 






*■ -^ . t ' 


'. -• ' 




IS* 


'*' 
























*' » . 














* - 






t 




*«• 
















































* 






1^ 


^ 


# 






^ *: 


' -'^ " 


. < 


1 


<$te 




i»^ 


'^•# 













'^ 




The Vicinity of v Carinae lEta Argois', /R 10 h. 41 m., Decl. S. 59° (photographed by- 
Bailey with the Bruce Telescope, 1896. Exposure 4 hours) 

428 



Proper Motio7is of the Stars 429 

catalogued. Each photograph covers an area of four square degrees ; 
and as duplicate exposures are necessary, the total number of plates 
will be not less than 25,000. The entire expense of this comprehensive 
map of the stars will exceed $2,000,000. The observatories of the 
United States have taken no part in this cooperative programme ; but 
by the liberality of Miss Bruce, the Observatory of Harvard College, 
which has a station in Peru also, has undertaken independently to chart 
in detail the more interesting regions of the entire heavens, with the 
Bruce photographic telescope, a photographers doublet consisting of 
four lenses, each 24 inches in aperture. A section of a recent chart 
obtained with this great instrument is shown opposite. The plates are 
14X 17 inches ; about two thousand wdll be required to cover the entire 
sky. On the original plate of which the illustration is part were counted 
no less than 400,000 stars. Also Kapteyn has measured and catalogued 
about 300,000 stars on plates taken at Capetown. 

Proper Motions of the Stars. — If Ptolemy or Kepler 
or any great astronomer of the past were alive to-day, 
and could look at the stars and constellations as he did in 
his own time, he would be able to discern no change what- 
ever in either the brightness of the stars or their apparent 
positions relatively to each other. Consequently they seem 
to have been well named 7?-r^<^ stars. If, however, we com- 
pare closely the right ascensions and declinations of stars 
a century and a half ago with their corresponding positions 
at the present day, we find that very great changes are 
taking place ; but these changes relatively to the imaginary 
circles of the celestial sphere are in the main due to pre- 
cessional motion of the equinox. A star's annual proper 
motion in right ascension is the amount of residual change 
in its right ascension in one year, after allowance for aber- 
ration, and motion of the equinox. The proper motion in 
declination may be similarly defined. Proper motion is 
simply an angular change in position athwart the line of 
vision, and may correspond to only a small fraction of the 
star's real motion in space. 

As a whole, proper motion of the brighter stars exceeds that of 
the fainter ones, because they are nearer to us : and proper motion is a 



430 



Stars and Cosmogony 



combined effect of the sun's motion in space and of the stars among 
each other. Ultimately these two effects can be distinguished. Still, 

even the largest proper mo- 
tion yet known, that of a star 
in Ursa Major, No. 1830 in 
Groombridge's catalogue, and 
often called the ^ runaway 
star,' is only 7''. 6; and nearly 
three centuries must elapse 
before it would seem to be 
displaced so much as the 
breadth of the moon. The 
average proper motion of 
first magnitude stars is about 
o".25 ; and of sixth magni- 
tude stars, only one sixth 
as great. Among European 
astronomers Auwers has con- 
tributed most to these critical studies, and Porter in America has 
published a catalogue of proper motions. 




Ursa Major now, and after 400 Centuries 



Secular Changes in the Constellations. — The accumu- 
lated proper motion of the stars of a given asterism will 
hardly change its naked-eye appearance appreciably within 
2000 years. But when intervals of 1 5 to 20 times greater 
are taken, the present well-known constellation figures 
will in many cases be seriously distorted. 



Particularly is this true of Cassiopeia, Orion, and Ursa Major. In 
the left-hand diagram above is shown the present asterism of the Dipper, 
to each star of which is attached an arrow indicating the direction and 
amount of its proper motion in about 400 centuries. The companion 
diagram at the right is a figure of the same constellation (according 
to Proctor) after that interval has elapsed : though much distorted, it 
would be recognized as Ursa Major still. As indicated by the direction 
of the arrows, the extreme stars. Alpha and Eta, seem to move alm.ost 
in the opposite direction from the others, and observations with the 
spectroscope confirm this result. As the spectra of the five intermediate 
stars are quite identical, it is likely that they originally formed part of 
a physically connected system. Most of the brighter stars of the 
Pleiades are also moving in one and the same direction, and this com_- 
munity of proper motion has received the name star drift. 



Apex of the Suns Way 431 

Apex of the Sun's Way. — When riding upon the rear 
platform of a suburban electric car, where the ties are not 
covered .under, observe that they seem to crowd rapidly 
together as the car swiftly recedes from them. If possible 
to watch from the front platform, precisely the opposite 
effect will be noticed : the ties seem to open out and sepa- 
rate from each other just as rapidly. In like manner 
the stars in one part of the celestial sphere, when taken by 
thousands, are found to have a common element of proper 
motion inward toward a center or pole ; while in the 
opposite region, they seem to be moving radially out- 
ward, as if from the hub and along the spokes of a wheel. 
This double phenomenon is explained by a secular motion 
of the sun through space, transporting his entire family of 
planets, satellites, and comets along with him. This hub 
or pole toward which the 
solar system is moving is 
called the sun s goal, or the 
apex of the suns way ; and 
recent determinations by L. 
Struve, Boss, and Porter 
make it practically coinci- 
dent with the star Vega. 
Similarly the point from 
which we are recedins: is 

^ Earth's Helical Path in Space 

known as the suns quit, 

and it is roughly a point halfway between Sirius and 
Canopus. So vast is this orbit of the sun that no deviation 
from a straight line is yet ascertained, although our motion 
along that orbit is about 12 miles every second. 

This result is verified both by discussion of proper motions, and 
by finding the relative movement of stars 'fore and aft' by means of 
the spectroscope. As yet, however, there is no indication of a ' central 
sun,' a favorite hypothesis in the middle of the 19th century. This 




432 Stars and Cosmogony 

motion of the sun does not interfere with the relations of his family 
of planets to him ; but simply makes them describe, as in the figure 
just given, vast spiral circumvolutions through interstellar space. 

Stellar Motions in the Line of Sight. — From a bridge 
spanning a rivulet, whose current is uniform, we observe 
chips floating by, one every 15 seconds. Ascending the 
stream, we find their origin : an arithmetical youth on the 
bank has been throwing them into mid-stream at regular 
intervals, four chips to the minute. We interfere with his 
programme only by asking him first to walk down stream 
for two minutes, then to return at the same uniform speed ; 
and to repeat this process several times, always taking 
care to throw the chips at precisely the same intervals as 
before. Returning to the bridge to observe, we find the 
chips no longer pass at intervals of 15 seconds as at first; 
but that the interval is less than this amount while the 
boy who tosses them is walking down stream, and greater 
by a corresponding amount while he is going in the oppo- 
site direction. By observing the deviation from 15 sec- 
onds, the speed at which he walks can be found. Similarly 
with the motions of stars toward or from the earth ; the 
boy is the moving star, and the chips are the crests of 
light waves emanating from it. When the star is coming 
nearer, more than the normal number of waves reach us 
every second, and a given line in the star's spectrum is 
displaced toward the violet. Likewise when a star is 
receding, the same line deviates toward the red. This 
effect was first recognized in 1842 by Doppler, from whom 
comes the name ' Doppler's principle.' Research of this 
character is an important part of the programme at Green- 
wich (opposite), and at the Yerkes Observatory (page 7). 

The spectral observation is an exceedingly delicate one ; but by 
measuring the degree of displacement of stellar lines, as compared with 
the same lines due to terrestrial substances artificially vaporized, the 
motions of about 100 stars toward or from the solar svstem have been 




V O 



Qc^ S P^ 






X 



c3 *-> 



.S S 



2 S 



.H S 



V O 



todd's astrcjn. — 28 



434 



Stars a7id Cosmogony 



ascertained. The limit of accuracy is two or three kilometers per 
second. The observed motions of stais, not situated at the poles of 
the ecliptic, or near them, require a correction depending on the earth's 
orbital motion round the sun. When thus modified, the motions of 
few stars in the line of sight exceed 40 kilometers per second. 

Motions of Individual Stars. — Chiefly by Huggins of 
London, Maunder at Greenwich, Vogel at Potsdam, Ger- 
many, and Keeler and Campbell at the Lick Observatory, 
have these researches been conducted. Below are results 
for a few stars showing best accordance : — 

Motions in the Line of Sight 



Star's Name 






Position for 1900.0 


Motion per Second 

TOWARD or from THE SuN 




R. A. 


Decl. 


Miles 


Kilometers 


Alpha Arietis 
Aldebaran 
Rip-el . . . 






h. m. 

2 2 

4 30 

5 10 
5 50 

10 14 
13 20 

15 30 
19, 46 


' 
N. 22 59 
N. 16 18 
S. 8 19 
N. 7 23 
N. 20 21 
S. 10 38 
N.27 3 
N. 8 36 


- II.7 
+ 31. 1 
+ 13.6 

+ 17-6 
-25.1 

- 10.6 
+ 20.3 
-239 


- 19 

+ 50 

+ 22 


Betelgeux 
Gamma Leonis 
Spica . 
Alpha Coronae 
Altair . . . 




+ 28 
-40 
- 17 
+ 33 
-38 



These are a tenth part of all successfully ascertained. 
Spectrum photography has contributed greatly to the con- 
venience and accuracy of these critical observations. 

Relation of Brightness to Distance of the Stars. — Were 
the stars all of the same real size and brightness, their 
apparent magnitudes, combined with their direction from 
us, would make it possible to state their precise arrange- 
ment throughout the celestial spaces. But all assumptions 
of this character are unfounded, and lead to erroneous 
conclusions. The very little yet known about the real dis- 



Stellar Distances 435 

tances of the stars and their motions, when taken in con- 
nection with their apparent magnitudes, proves conclusively 
that many of the fainter stars are relatively near the solar 
system ; also that several of the brighter stars are exceed- 
ingly remote, and therefore exceptionally large and massive. 
Apparent brightness, therefore, is no certain criterion of 
distance. This subject of investigation is so vast and 
intricate that very little headway has yet been securely 
made. What we really know may be put in a single brief 
sentence : Only as a very general rule is it true that the 
brighter stars are nearer and larger than the great mass 
of fainter ones ; and to this rule are conspicuous and im- 
portant exceptions. Our knowledge is rather negative than 
positive; and we may be certain that (i) the stars are far 
from equally distributed throughout space, and (2) they 
are far from alike in real brightness and dimensions. 

How Stellar Distances are found. — Recall the instance of 
the earth and moon (page 237): we found the moon's dis- 
tance from us by measuring her displacement among the 
stars, as seen from two observatories at the ends of a diam- 
eter of our globe, or as near its extremities as convenient. 
But this earth is so small, that, as seen from a star, even its 
entire diameter would appear as an infinitesimal ; we must 
therefore seek another base line. Only one is feasible ; 
and although 25,000 times greater, still it is hardly long 
enough to be practicable. 

Imagine the earth replaced by a huge sphere, whose circle equals 
our orbit round the sun. From the ends of a diameter, where we are 
at intervals of six months, we may measure the displacement of a star, 
just as we measured the displacement of the moon from the two ob- 
servatories. We find, then, that half this displacement represents the 
star's parallax, just as half the moon's displacement gave the lunar 
parallax. And just as in the case of moon, sun, and planets we em- 
ploy the term diiLrnal parallax, so in the case of stars we call animal 
parallax the angle at the star subtended by the radius of earth's orbit. 
Measurement of a star's annual parallax is one of the exceedingly diffi- 



436 



Stars and Cosmogony 



T H E S T S r 



..I • * 
I 
I 



DISTANT 
STAR 



i FARTHER 
? STAR 



NEAR^ 
STAR 



I \ 



cult problems that confront the practical astronomer ; so small is the 
angle that its measurement is much as if a prisoner whp could only look 
out of the window of his cell were given instruments of utmost pre- 
cision and compelled to as- 
certain the distance of a 
mountain 20 miles away. 

A Star's Parallactic El- 
lipse. — Stand a book on 
the table, and place the eye 
about two feet from the side 
of it. Hold the point of a 
pen or pencil steadily, at 
distances of about 5, 10, 
and 20 inches from the eye, 
and between it and the 
book. For each position of 
the pencil move the head 
around in a nearly vertical 
circle about two inches in 
diameter, noticing in each 
case the size of the circle 
which the pen point appears 
to describe where projected 
on the book. This con- 
clusion is quickly reached : 
the farther the pencil from 
the eye, the smaller this cir- 
cle. Now imagine the eye 
replaced by the earth in its 
orbit (as at the bottom of 
the diagram), the pencil by 
the three stars shown, and 
the book by the farthest 
stars. Evidently the earth 
by traveling round the sun 
makes the stars appear to de- 
scribe elliptic orbits whose 
size is precisely proportioned inversely to their distance from the solar 
system. The eccentricity of the parallactic ellipse of a star is exactly 
the same as that of its aberration ellipse already figured on page 164: 
a star at the pole of the ecliptic describes a circle, and those situated 
in the ecliptic simply oscillate forth and back in a straight line. Stars 
in intermediate latitudes describe ellipses whose eccentricities are de- 
pendent upon their latitude. There are these two important differ- 



1 / 




Hd theS^ 



The Nearest Star describes the Largest Apparent 
Ellipse among the Farthest Stars 



Stellar Distances 



437 



ences : (i) in the aberration ellipse, the star is always thrown 90° 
forward of its true position, while in the parallactic ellipse, it is just 180° 
displaced ; (2) the major axis of the aberration ellipse is the same for 
all stars, but in the parallactic ellipse its length varies inversely with 
the distance of the star. Measurement of the major axis of this ellipse 
affords the means of ascertaining how far away the star is, because the 
base line is the diameter of the earth's orbit. This is called the differ- 
ential method^ because it determines, not the star's absolute parallax, 
but the difference between its parallax and that of the remotest star, 
assumed to be zero. Researches on stellar distances have been prose- 
cuted by Gill at Capetown and Elkin at Yale Observatory with a high 
degree of accuracy by the heliometer. 

The Distance of 61 Cygni. — The star known as 61 Cygni has 
become famous, because it is the first star whose distance was ever 
measured. This great step in our knowledge of the sidereal universe 
was taken about 1840 by the eminent German astronomer Eessel, 
often called the father of practical astronomy, because he introduced 
many far-reaching improvements conducing to higher accuracy in 
astronomical methods and results. This star is a double star, standing 
at an angle with the hour circle (north-south), as the diagram shows. 
Two small stars are in the same field of view, a and b^ nearly at right 
angles in their direction from the double star ; and Bessel had reason 
for believing that they were 

vastly farther away than 61 north 

Cygni itself. So at opposite 
seasons of the year he meas- 
ured with the heliometer the 
distances between each of 
the components of 61 Cygni 
and both the stars a and b. 
What he found on putting 
his measures together was 
that these apparent distances 
change in the course of the 
year ; and that the nature of 
the change was exactly what 
the star's position relatively to the ecliptic led him to expect. The 
measured amount of that change, then, was the basis of calculation of 
the star's distance from our solar system. Within recent years pho- 
tography has been successfully applied to researches of this character, 
with many advantages, including increased accuracy of the results, 
particularly by Pritchard. 

Illustration of Stellar Distances. — The nearest of all the fixed 
stars is Alpha Centauri, a bright star of the southern hemisphere. Its 



*6l 



*a 



Bessel's Measures of Distance of 61 Cygni 



438 Stars and CosTUogony 

parallax is o'^75, and it is 275,000 times more distant from our solar 
system than the sun is from the earth. But there is little advantage in 
repeating a mere statement of numbers like this. Try to gain some 
conception of its meaning. First, imagine the entire solar system as 
represented by a tiny circle the size of the dot over this letter /'. 
Even the sun itself, on this exceedingly reduced scale, could not be 
detected with the most powerful microscope ever made. But on the 
same scale the vast circle centered at the sun and reaching to Alpha 
Centauri would be represented by the largest circle which could be drawn 
on the floor of a room 10 feet square. Or the relative sizes of spheres 
may afford a better help. Imagine a sphere so great that it would 
include the orbits of all the planets of the solar system, its radius being 
equal to Neptune's distance from the sun. Think of the earth in compari- 
son with this sphere. Then conceive all the stars of the firmament as 
brought to the distance of the nearest one, and set in the surface of a 
sphere whose radius is equal to the distance of that star from us. So 
vast would this star sphere be that its relation to the sphere inclosing 
the solar system would be nearly the same as the relation of this latter 
sphere to the earth. When studying the sun and the large planets, it 
seemed as if their sizes and distances were inconceivably great ; but 
great as they are, even the solar system itself is as a mere drop to the 
ocean, when compared with the vastness of the universe of stars. 

The Unit is the Light Year. — In expressing intelligently 
and conveniently a distance, the unit must not be taken too 
many times. We do not state the distance between New 
York and Chicago in inches, or even feet, but in miles. 
The earth's radius is a convenient unit for the distance of 
the moon, because it has to be taken only 60 times ; but 
it would be very inconvenient to use so small a unit in 
stating the distances of the planets. By a convention of 
astronomers, the mean radius of our orbit round the sun is 
the accepted unit of measure in the solar system. Simi- 
larly the adopted unit of stellar distance is, not the distance 
of any planet nor the distance of any star, but the distance 
traveled by a light wave in a year. This unit is called 
the light yeai'. 

The velocity of light is 186,300 miles per second, and it travels from 
the sun to the earth in 499 seconds. The light year is equal to 



Distances of Well-known Stars 



439 



63,000 X 93,000,000 miles, because the number of seconds in a year is 
about 499 X 63,000; or, the light year is equal to 5 J trillion miles. 
Obviously, as stellar parallax has a definite relation to distance, parallax 
must be related to the light year also : the distance of a star whose 
parallax is \" is about 3^ light years. So that, if we divide 2>\ by the 
parallax (in seconds of arc), we shall have the star's distance in light 
years. 

Distances of Well-known Stars. — Although the paral- 
laxes of more than a hundred stars have been measured, 
only about 50 are regarded as well known. Twelve are 
given in the following table, together with their corre- 
sponding distance in light years: — 

Stellar Distances and Parallaxes 



Star's Name 


Q 

s 

< 


Approximate 
[1900.0] 


Proper 
Motion 


Paral- 
lax 


Distance in — 


R. A. 


Decl. 


Light 
Years 


Trillions 
OF Miles 






h. m 


' 


.' 








a Centauri . . . 


— O.I 


14 zi 


S. 60 25 


Z'^1 


0.75 


4i 


25 


61 Cygni .... 


5-1 


21 2 


N.38 15 


5.16 


045 


7i 


43 


Sirius .... 


-1.4 


6 41 


S. 16 35 


I-3I 


0.38 


8i 


50 


Procyon .... 


0-5 


7 34 


N. 5 29 


1.25 


0.27 


12 


71 


Altair 


0.9 


19 46 


N. 8 36 


0.65 


0.20 


16 


94 


o"^ Eridani . . . 


44 


4 7 


S. 7 7 


4.05 


0.19 


17 


100 


Groombridge 1830 


6.5 


II 7 


N. 38 32 


7.65 


0.13 


25 


147 


Vega 


0.2 


18 34 


N. 38 41 


0.36 


0.12 


27 


158 


Aldebaran . . . 


I.O 


4 30 


N. 16 18 


0.19 


O.IO 


32 


191 


Capella .... 


0.1 


5 9 


N.45 54 


0.43 


O.IO 


32 


191 


Polaris .... 


2.1 


I 23 


N. %% 46 


0.05 


0.07 


47 


276 


Arcturus .... 


0.2 


14 II 


N. 19 41 


2.00 


0.02 


160 


950 



Most of these are bright stars, but a considerable number 
of faint stars have large parallaxes also. Relative distances 
and approximate directions from the solar system are shown 
in next ilhistration, for a few of the nearer and best deter- 



440 



Stars and Cosmogony 



mined stars. The scale is necessarily so small that even 
the vast orbit of Neptune has no appreciable dimension. 
The outer circle corresponds nearly to a parallax o.^^i. 
The distances of many stars have been ascertained by 
Sir Robert Ball. Various determinations often differ 
widely. 




Distances of Stars from the Solar System in Light Years (according to Ranyard 

and Gregory) 

Dimensions of the Stars. — After we had found the distance of the 

sun and measured the angle filled by his disk, it \Yas possible to calcu- 
late his tRie dimensions. But this simple method is inapplicable to the 
stars, because their distances are so vast that no stellar disk subtends 
an appreciable angle. Indirect means must therefore be employed to 
ascertain their sizes ; and it cannot be said that any method has yet 
yielded very satisfactory results. Combining known distance with 
apparent magnitude, Maunder has calculated the absolute light-giving 
power of the following stars, that of the sun being unity : — 



Types of Stellar Spectra 



441 



SiRiAN Stars 

Procyon 25 

Altair 25 

Sirius 40 

Regulus no 

Vega 2050 



Solar Stars 

Aldebaran 70 

Pollux 170 

Polaris 190 

Capella 220 

Arcturus 6200 



But these are far from indicating their real magnitudes ; for amount of 
light is dependent upon intrinsic brightness of the radiating surface, 
as well as its extent. Among the giant stars are Arcturus, possibly a 
hundredfold the sun's diameter ; also Vega and Capella, likewise much 
larger than the sun. Algol, too, must have a diameter exceeding a 
million miles, and its dark companion (page 450) is about the size of 
the sun — results reached by means of the spectroscope, which measures 
the rate of approach and recession of Algol when the invisible attendant 
is in opposite parts of its orbit. The law of gravitation gives the mass 
of the star and size of its orbit, so that the length of the eclipse tells 
how large the dark, eclipsing body must be. 

Types of Stellar Spectra. — Sir William Huggins in 1864 
first detected lines indicating the vapor of hydrogen, cal- 
cium, iron, and sodium in the atmospheres of the brighter 
stars. Stellar spectra have been classified in a variety of 
ways, but the division into four types, proposed in 1865 by 
Secchi, has obtained the widest adoption. They are illus- 
trated on the next page : — 

Type I is chiefly characterized by the breadth and inten- 
sity of dark hydrogen lines ; also a decided faintness or 
entire lack of metallic lines. Stars of this type are very 
abundant. They are blue or white ; Sirius, Vega, Altair, 
and numerous other bright stars belong to this type, often 
called Sirian stars, a class embracing perhaps more than 
half of all the stars. 

Type 11 is characterized by a multitude of fine dark, me- 
tallic lines, closely resembling the solar spectrum. They are 
yellowish like the sun ; Capella and Arcturus (page 445) 
illustrate this type, often called the solar stars, which are 
rather less numerous than the Sirian stars. According to 



442 



Stars and Cosmogony 



recent results of Kapteyn, absolute luminous power of 
first type stars exceeds that of second type stars seven- 
fold ; and stars least remote from the sun are mostly of 
the second type. 



^^^ 



Red 



] 



Type I — Sirius 




Type li — Capelia and the Sun 




Type 111— Alpha Herculis 





Violet 



Type IV — 152 Schjellerup 
Secchi's Four Types of Stellar Spectra 



Red 



Type III is characterized by many dark bands, well de- 
fined on the side toward the blue, and shading off toward 
the red end of the spectrum — a ' colonnaded spectrum,' 
as Miss Gierke very aptly terms it. Orange and reddish 
stars, and a majority of the variables, fall into this cate- 
gory; Alpha Herculis, Mira, and Antares are examples of 
this type, 



Stellar Spectrum Photography 443 

Type IV is characterized by dark bands, or flutings as 
they are often technically called, similar to those of the 
previous type, only reversed as to shading — well defined 
on the side toward the red, and fading out toward the blue. 
Stars of this type are few, perhaps 50 in number, faint, 
and nearly all blood-red in tint. Their atmospheres con- 
tain carbon. 

Type V has been added to Secchi's classification by 
Pickering, and is characterized by bright lines. From two 
French astronomers who first investigated objects of this 
class, they are known as Wolf-Rayet stars. They are all 
near the middle of the Galaxy, and their number is about 
70. They are a type of stellar objects quite apart by 
themselves, of which Campbell has made an especial 
study. Many objects called planetary nebulae yield a 
spectrum of this type. 

A classification by Vogel combines Secchi's types III 
and IV into a single type. It is not yet determined 
whether these differences of spectra are due to different 
stages of development, or whether they indicate real differ- 
ences of stellar constitution. Most likely they are due to 
a combination of these causes. 

How a Star's Spectrum is commonly photographed. — The light of 
a fixed star comes to the earth from a definite point on the dome of the 
sky. so that a stellar image, when produced by the object glass of a 
telescope, is also a point. Now suppose that a glass prism is attached 
to the telescope in front of its objective, as was first done in 1824, by 
Fraunhofer, and consider what takes place ; the light of the star first 
passes through this prism, called the ^ objective prism,' and then 
through the object glass, which brings the rays all to a focus. The 
star's image, however, is no longer a point, but spread out into a line, 
made up of many colors from red to violet. It is at this focus that 
the sensitive dry plate is inserted, and allowed to remain until the ex- 
posure is judged sufficient to produce the desired impression. Perhaps 
three hours are necessary ; and during all this time the adjustment of the 
photographic telescope is so maintained that when the plate is de- 
veloped, the spectra of all the stars will appear, not as lines, but as tiny 




444 Stars and Cosmogony 

rectangular patches, or bits of ribbon with light stripes across them. A 
25th part of such a negative is here pictured, as obtained with the Bache 

telescope of the Boyden Observatory, 
by exposure in 1893 to the stars of 
the constellation Carina. On it were 
1000 spectra sufficiently distinct for 
classification. 

The Draper Catalogue. — With 
an identical instrument, similarly 
equipped with prisms, stellar spec- 
trum photography has been vigo- 
rously conducted at Harvard College 
Observatory since 1886. The prisms 
are mounted with their edges east 
and west ; and the clock motion is 
regulated according to the degree of 
dispersion employed, as well as the 
magnitude and color of the stars 

^ ^, • ^ • ,D- 1 • N in the photo«:raphic field. Upon a 

Spectra of Stars in Carina (Pickering) . ^ K r ^ ^ ^ 

(Exposure 2 h. 20 m.) smgle plate are often many hundred 

spectra ; and in studying them, the 
great advantage of such close juxtaposition is at once apparent. For 
example, the spectra of about 50 stars in the Pleiades show at a 
glance practical identity of chemical composition. These researches, 
conducted under the superintendence of Edward C. Pickering, at the 
charges of a fund provided by Mrs. Draper as a memorial to her 
husband, gave to astronomers in 1890 the ^Draper Catalogue of stellar 
spectra,^ including more than 10,000 stars down to the eighth magnitude. 
Nearly all the tedious and time-consuming labor of examining the 
plates was performed by Mrs. Fleming, Miss Maury, and others. This 
comprehensive system of registering spectra naturally paved the way 
for a more detailed classification of the stars than Secchi's ; and with 
subsequent work at the same observatory, has led to their division into 
about 20 groups. Also the peculiarities of spectra have led to the 
detection of numerous variable stars, and several new or temporary 
stars (page 448) . 

Stellar Spectra of High Dispersion. — Vega is the first star whose 
spectrum was successfully photographed by Henry Draper in 1872. 
Brightest stars afford sufficient light for the photography of their 
spectra, even after a high degree of dispersion by a train of several 
prisms, or by a diffraction grating. Multitudes of lines are thus re- 
corded, especially in stars of the solar type. A part of the photo- 
graphic spectrum of Arcturus is shown on next page, almost a duplicate 
of the solar spectrum. In addition to the fine results obtained at 



Variable Stars 

Cambridge by Pickering, and at South Kensington by Sir 
Norman Lockyer, must be mentioned those of Vogel and 
Scheiner at Potsdam, near Berlin ; and of Deslandres at 
Paris, who has lately detected in the spectrum of Altair a 
series of fine, bright, double lines, bisecting the dark hydro- 
gen and other bands. He regards them as indication that 
this star is enveloped by a gaseous medium like that of the 
solar chromosphere. 

Variable Stars. — A star whose brightness has 
been observed to change is called a variable star, 
or simply a ' variable.' Nearly looo such objects 
are now recognized. This change may be either 
an increase or a decrease ; and it may take place 
either regularly or irregularly. Other classes of 
variables rise and fall in different ways : some ex- 
hibiting several fluctuations of brightness in every 
complete period (like Beta Lyrae, a well known 
variable whose spectrum presents a complexity 
of hydrogen lines and helium bands now under 
investigation by Frost) ; some in simple periods 
only a few hours (the shortest at present known 
is U Pegasi, ^\ hours) ; others changing slowly 
through several months. In general the last, 
which are usually reddish in tint, change as 
rapidly when near minimum as when near maxi- 
mum, their light-curves being like deep waves 
with sharp crests. Astronomers term these 'Omi- 
cron Ceti variables,' after the type star of this 
name, also known as Mira, or *the marvelous,' 
whose variability has been known for three cen- 
turies. Their average period is about a year, and 
perhaps half of the recognized variables are of 
this type. Allied to them are the temporary stars 
described in a subsequent section. Of a type 
whose variation is the reverse of Mira are the 



445 



446 



Stars and Cosmogony 



'Algol variables,' about 20 in number, whose light sud- 
denly drops at regular intervals, as if some invisible body- 
were temporarily to intervene. 

Knowledge of the variable stars has been greatly advanced by the 
labors of Chandler and Sawyer, of Cambridge. Chandler's catalogues 
contain about 500 classified variables. Such an object, previously with- 
out a name, is designated by letters R, S. T. U. and so on. in order 
of discovery in the especial constellation where found. The average 
range in recently discovered variables is less than one magnitude. 

Distribution and Observation of Variables. — As to their distribution 
over the heavens, variable stars are most numerous in a zone inclined 
about 18^ to the celestial equator, and split in two near where the cleft 
in the Galaxy occurs. Almost all the temporary stars are in this duplex 
region. A discovery of much significance was made by Bailey, in 1896, 
of an exceptional number of variables among the components of stellar 
clusters, more than 100 being found among the stars of a single 
cluster; and the mutations of magnitude are marked within a few hours. 
Variables are most interesting objects, and observations of great value 
may be made by amateurs. First the approximate times of greatest or 
least brightness must be ascertained : these are given each year in the 
^ Companion ' to The Observatory (edited by Turner and published at 
Greenwich), and in Popular Astronomy (published monthly by Payne 
at Northfield. ^Minnesota) . Following are a few variables, easily found 
from star charts : — 

Variable Stars 





Position 


(1900 0) 


Variation 




Star's Name 












Type of 










1 


Variable 




R. 


A. 


Decl. 


Period 


Range 




Omicron Ceti . 


h. 
2 


m. 
14 


S. 326 


Davs 
331 


^Magnitude 

,1.7 to 9.5 


Mira. 


Beta Persei . . 


3 


2 


N. 40 34 


H 


2.3 to 3.5 


Algol. 


Zeta Geminorum 


6 


58 


N. 20 43 


\o\ 


.3.7 to 4.5 




R Leonis . . . 


9 


42 


N. II 54 


313 


15.2 to 10 




Delta Librae . . 


14 


56 


S. 8 7 


2} 


1 5 to 6.2 


Algol. 


Alpha HercuHs . 


17 


10 


N. 14 30 


90 i 


3.1 to 3.9 


Irregular. 


X Sagittarii . . 


17 


41 


S. 2748 


7 


4 to 6 




Beta Lyr^ . . 


18 


46 


N. 33 15 


12.9 


3-4 to 4-5 




Delta Cephei 


22 


- 


>^'- 57 54 


5} 


3.7 to 4.9 





Temporary, or New Stars 447 

A small telescope or opera glass is a distinct help in observing a 
variable. When its brightness is changing, repeated comparison and 
careful record of its magnitude with that of other stars in the same 
tield, will make it possible to ascertain the time of maximum or mini- 
mum. Such observations are of use to the professional investigator of 
periods of variable stars. 

Temporary Stars, or New Star-s. — A variable star which, 
usually in a few weeks' time, vastly increases in brightness, 
and then slowly wanes and disappears entirely, or nearly 
so, is called a temporary star. Accounts of several such 
are contained in ancient historical records. In the Chinese 
annals is an allusion to such an outburst in Scorpio, B.C. 134; 
it was observed by Hipparchus, and led to his construc- 
tion of the first known catalogue of stars, made with refer- 
ence to the detection of similar phenomena in the future. 
Tycho Brahe carefully observed a remarkable object of 
this class near Cassiopeia, which, in the latter part of 1572, 
surpassed the brightness of Jupiter, was for a while visible 
in broad daylight, and, in a year and a half, had completely 
disappeared. In 1604-5 ^ i^^w star of equal brightness 
was seen by Kepler in Ophiuchus ; it also disappeared. 
None were recorded in the i8th century. Similar and 
equally remarkable objects made their appearance, and 
passed through like stages near our own day in — 

1866 in Corona Borealis ; 

1876 in Cygnus ; 

1885 in the Great Nebula in Andromeda; 

1891-92 in Auriga. 

Such a star is often called Nova, with the genitive of its 
constellation added, as Nova Cygni. Temporary stars 
remain unchanged in apparent position during their great 
fluctuations of brightness, and no new star has been found to 
have a measurable parallax. Probably Nova Andromedae 
was connected with the nebula in which it appeared. The 
new stars of 1866 and 1892, after dropping to a low tele- 



448 Stars and Cosmogony 

scopic magnitude, had a secondary rise in brightness, 
though not to their original magnitude, after which they 
faded to their present condition as very faint telescopic 
objects". Nova Aurigae has become a faint nebulous 
star. Thorough search by Mrs. Fleming of the photo- 
graphic charts and spectrum plates of the Harvard College 
Observatory, obtained in both hemispheres, has led to the 
detection of many new stars that would otherwise have 
escaped observation. Recent ones are Nova Normae 
(1893), Nova Carinae (1895), and Nova Centauri (1895). 
Following are spectra of temporary stars, showing hydro- 
gen and calcium lines. 




Spectra of New Stars i Pickering) 



Spectra of New Stars. — The spectroscope has proved itself a power- 
ful adjunct in the observation of temporary stars. First employed on 
the Nova of 1866, it demonstrated the presence of incandescent hydro- 
gen. Nova Cygni, ten years later, gave a similar spectrum, added to 
which were the Hues of helium, long known in the sun, but only in 1895 
identified as a terrestrial element. Nova Andromedae (1885) to most 
observers presented a continuous spectrum; but Nova Aurigae (1892) 
gave a distinctly double and singularly complex spectrum. Many pairs 
of lines indicated clearly a community of origin as to substance, and 
accurate measurement showed a large displacement which indicated a 
relative velocity of nearly 900 kilometers, or more than 500 miles per 
second ; and this type of spectrum remained characteristic for more 
than a month. For each. bright hydrogen line displaced toward the 
red there was a dark companion line or band, about equally displaced 
toward the violet. It was as if the strano^e lidit were due to a solid 



Variables of the Algol Type 



449 



globe moving swiftly away from us, and plunging into an irregular 
nebulous mass swiftly approaching us. Tests for parallax placed Nova 
Aurigae at the distance of the Galaxy, so that this marvelous celestial 
display must actually have occurred in space as remotely as the begin- 
ning of the 19th century. Nova Normae was characterized by a spectrum 
almost identical with that of Nova Aurigae, as shown in the photographs 
opposite, taken in Cambridge and Peru. 

Irregular Variables. — These objects are not numerous, but some of 
them are very remarkable ; for example. Eta Argus, an erratic variable 
in the southern hemisphere (shown in the midst of the nebulosity on 
page 428). Halley, who visited Saint Helena in 1677, recorded its mag- 
nitude as the fourth. Between 1822 and 1836 it fluctuated between the 
first and second magnitudes; but in 1838 the light became tripled, 
rivaling all the stars except Sirius and Canopus. In 1843 i^ was even 
brighter, but since then it has declined more or less steadily, reach- 
ing a minimum of the ']\ magnitude in 1886. Probably it has no 
regular period, although one of a half century has been suggested. 
Recently the brightness of Eta Argus has shown a slight increase. 
A few^ other stars vary in this irregular manner, though their fluctuations 
are confined to a much narrower range. 

Variables of the Algol Type. — Algol is the name of 
the star Beta Persei, the best known object of this class. 
As a rule, the periods of this 
type of variables are short, 
and they remain at maximum 
brightness during nearly the 
whole. Then almost suddenly 
they drop within a few hours 
to minimum light, remain there 
but a fraction of an hour, and 
almost as rapidly return to full 
brightness again. The spectra 
of all Algol variables are of 

Light-Curves near Minimum of Four 
the first type. Algol variables (Pickering) 



[^ 


$^^|K;2 -i 6 -t-i +2>'3' 


^^/^.. 


■0.4 \ 


\ \ \ / / / 


/ ' 0.4- 


-0.6 N 


\ \ ^^ / / 


> 0.6- 


-0.8 


\. \ WoPHiucyl / 


/ 0.8 • 


-1.0 


\ \ ^-^ / / 


-0- 


•1.2 


\\ /3 PERSEI / / 


1.2 


■1.4 


\\ // 


1.4- 


■1.6 


\\ // 


1.6 


-1.8 


\l // 


1.8 • 


•2.0 


\ r 


2.0- 


-2.2 


\ / 


2.2- 


2.4 
2.6 


l7cipHiy^ 


2.4- 
2.6- 


■2.8 


TFdelphini 


2.8- 



The diagram represents the light-curves (between maximum and 

minimum) of four stars of this type, as determined by E. C. Pickering 

at the Harvard College Observatory. The star W Delphini, although 

telescopic, is the most pronounced object of this type so far discovered. 

todd's astron. — 29 



45 o Stars a7id Cosmogony 

It remains at full brightness rather more than four days ; then from the 
9.3 magnitude (upper left-hand corner of the diagram) it drops in 
seven hours to the 12.0 magnitude, becoming so faint as to be invisible 
in a four-inch telescope. Algol, in 4^ hours, drops a little more than i .0 
magnitude, and returns to its full brightness in 5^- hours, as the curve 
shows. Its period, or interval from one minimum to the next, is very 
accurately known; at present it is 2 d. 20 h. 48 m. 55.4 s., and is very 
gradually lessening. At full brightness Algol is of the 2.2 magnitude, 
and is therefore a conspicuous star. It remains at minimum only about 
15 minutes. Algol is best observed from early autumn to the middle of 
spring. Belonging to a type now recognized as new, though at first 
classified with Algol stars, are a few such rapid variables as S Antliae 
which was discovered by Paul in 1888. These compound stars would 
seem to constitute a binary system whose members swing round each 
other almost in contact (page 469). 

Causes of Variability. — No general explanation seems 
possible covering the variety in mutations of brightness of 
all classes of variables. Those of ttie 
Algol type are readily accounted for by 
the theory of a dark eclipsing body, 
smaller than the primary, and traveling 
round it in an orbit lying nearly edgewise 
to us. The illustration shows this : in 
the upper figure the system appears as 
we look at it ; in the lower, as it would 
Orbit of Algol's Dark appear if wc could look vertically upon 

Companion -^ -^ , . . '' 

it. Gravitation of a massive dark com- 
panion would, by its movement round Algol, displace it 
alternately toward and from the earth, when in the posi- 
tions E and F\ because the tw^o bodies must revolve round 
their common center of gravity. Just such a motion of 
Algol in the line of sight has been detected with the 
spectroscope, proving that the star alternately recedes 
from and advances toward us at the rate of 26 miles per 
second, in a period synchronous with that of its variability. 

For variables of other types, a comprehensive explanation is found in 
vast areas of spots, similar to spots on the sun, taken in connection with 




Double Stars 



451 



the star's rotation on its axis and a periodicity of the spots themselves. 
The new stars are more Ukely due to tremendous outbursts of glowing 
hydrogen ; perhaps in some cases to vaporization of dark bodies caused 
by their brushing past each other, or to a faint star's actual plunging 
through a gaseous region of space. Sir Norman Lockyer's theory for 
variables of the Omicron Ceti 
class is made clear by the 
illustration : variable stars are 
still in the condition of me- 
teoric swarms ; and the or- 
bital revolution of lesser 
swarms around larger aggre- 
gations must produce multi- 
tudes of collisions, periodically 
raising hosts of meteoric 
particles to a state of incan- 
descence. 

Double Stars. — Many 
stars which to the unas- 
sisted eye look simply as 
one, are separated by the 
telescope into more than one. According to the number, 
these are called double, triple, quadruple, or multiple stars. 
When the components of a pair appear to be associated 
together in space, it is catalogued as a double star. A few 
stars, however, are only apparently double, having no actual 
relation to one another in space, and only seeming in 
proximity because they happen to be nearly in the line of 
sight from the earth. They are remote from each other, 
as well as from the solar system. Such pairs of stars are 
called optical doubles. 




Sir Norman Lockyer's Meteoritic Theory of 
Variables 



Although a few double stars were known earlier, history of the dis- 
covery and measurement of these objects may be said to have begun 
with Sir William Herschel in 1779. The Struves, father and son, and 
Baron Dembowski, among others, have prosecuted these researches 
vigorously. More than 10,000 double stars are now known, and discov- 
eries have been rapidly made in recent years, particularly by Burnham 
of Chicago. The next illustration shows a dozen of the easier doubles, 



452 



Stars a7id Cosmogony 



within reach of small telescopes. Instruments of greater diameter 
than six inches are necessary to divide the components of a double 
star whose apparent distance from one another is less than o".^. Bond 
and Gould were pioneers in the application of photography to observa- 
tion of the wider ' doubles ' ; but here the assistance of this new method 
is not as important as in other departments of astronomy. Among 
other European observers of double stars are Bigourdan of Paris and 
Glasenapp of Saint Petersburg; and in America A. Hall, Comstock, 
and Leavenworth. 

Binary Stars. — Careful and protracted observations are 
necessary to determine the class to which any pair of 
stars belongs. If the components of a ^ double ' are 



' 1 


y AndrptnedcB 




• 


■i 

J^oltxris 




1 
•• 




•• 


• 

• 


CCL 


star 


£ HifdrcB. 


y Leonis 


Cor Cctroli 


^§ 


^3 












• 


• 


• • 


e Bootis 


/3 Scorpiv 


• 
OL- HerctxUs 


GlCjf^n-i 





Twelve Typical Double Stars 

found to revolve in a closed or elliptic orbit, they are 
called a binary star. It is assumed, and doubtless rightly, 
that this motion depends upon gravitation. 



About 200 binaries are now known, and the orbits of perhaps 50 of 
them are well ascertained. In his Researches on the Evolution of the 
Stellar Syste?ns (1896), See has presented a summary of present knowl- 
edge of these bodies. According to Miss Everett's investigation, the 
planes of their orbits sustain no definite relation to any fundamental 



Masses of Binary Stars 



453 



plane of the heavens. The star known as ^ 883 (star No. 883 dis- 
covered by Burnham) is the shortest known binary, its period being 
5 1 years ; the longest is Zeta Aquarii, not less than 1500 years. Several 
binary stars are recognized, one component of which is dark. These 
can be discovered only by the effect which the attraction of the dark 
star produces in changing the position of the bright one. The giant 
Sirius is a star of this kind, having a faint attendant only bright enough 
to be detected with large telescopes, and known as the companion of 
Sirius. Its orbit as determined by Burnham from observations 1862-96 
is shown adjacent. Before actual discovery (by A. G. Clark in 1862), 
not only its existence but its true position had been predicted by Auwers. 
The companion's period is 52 
years ; and its motion, and 
distance both from Sirius and 
from the solar system, show 
that the mass of the com- 
panion equals that of the sun, 
while that of the Dog Star it- 
self exceeds that of the sun 
i\ times. 



But the best known 
binary system is the 
one first discovered (by 
Richaud in 1689), Al- 
pha Centauri, also the 
nearest of all the fixed stars, 
first and second magnitude. 





1S0° 








V 


^ 


\ 




\ . 




V 




— — ~ 


V ^^Q2 






xXN^ 


'^x^r^"^^^" 


■~^-^ 






\\X 


^\^ 


^~^«J^see 





N 


• \ 


0\ 


^/'^'° 






"^ 


■^^\*^ 


/r. 



Orbit of Sirius (Burnham) 



Its components are of the 
The period of the stars' 
revolution is 81 years, the masses of the two components 
are very nearly equal, and their combined mass is twice 
that of the sun. The stars of a binary system are said to 
be in periastron when nearest to one another in space ; 
and in apastron when farthest. At periastron the com- 
ponents of Alpha Centauri are about as far apart as Saturn 
is from the sun ; in apastron their distance from each 
other greatly exceeds that of Neptune from us. 

Eccentricities and Masses of Binary Stars. — The orbits 
of binary stars are remarkable for great eccentricity ; also 
for the large mass-ratios of their components, always 



454 Stars and Cosmogony 

comparable, and in some cases nearly equal. In these 
respects they differ greatly from the bodies of the planet- 
ary system, the orbits in which are nearly circular, and 
none of the planets have more than a small fraction of 
the sun's mass. See explains the exceptionally high 
eccentricity of binary orbits, according to the principles 
of tidal evolution, from orbits which were nearly circular 
in the beginning. Originally the system was a single 
rotating nebulous mass, which became modified into a 
dumb-bell figure as a result of its own contraction. The 
average eccentricity of the best known binaries is 0.48, 
while that of the planets and satellites in our system is 
less than 0.04, or only yV as great ; and this extraordinary 
relation may be accepted as the expression of a funda- 
mental law of nature. Recalling the principles by which 
the mass of a planet is compared with that of the sun, it 
is evident that a like method will give the mass of a binary 
system, also in terms of the sun. First we must measure 
the major axis of the orbit, and observe the period of revo- 
lution ; also it is necessary to assume that the Newtonian 
law of gravitation governs their motion. Then : — 

rMoon's distance"]^ TDistance between components"!^ 

L from earth J L of Alpha Centauri J 



[Moon's sidereal!^ FEarth's mass! fPeriod of their i'^ f Sum of masses i 
period J L -f moon's J L revolution J Lof componentsj 

Masses of the few binary systems ascertained in this man- 
ner are about twofold or threefold that of the sun. 

Binaries discovered by the Spectroscope. — It was Bessel 
who first wrote of the ' astronomy of the invisible,' and 
his prediction has been marvelously fulfilled by the recent 
discovery of spectroscopic binaries. They are binaries 
whose components are so near each other that the tele- 
scope cannot divide them, and whose spectra therefore 
overlie. As the orbits of binary systems stand at all pos- 



Multiple Stars 455 

sible angles in space, a few will appear almost edge on. 
Let the two components be in conjunction, as referred to 
the solar system ; clearly their spectra will be identical. 
But when they reach quadrature, one will be receding 
from the earth and the other coming toward it. A given 
line in the compound spectrum, then, will appear double, 
on account of displacement due to motion of the compo- 
nents in opposite directions. Measure the displacement, 
and observe the period of its recurrence. This gives the 
velocity of the components relatively to each other, the 
dimensions of their orbit, and their mass in terms of the 
sun, always assuming that the same law of gravitation is 
regnant among the stars. 

The binaries so far discovered by this method have relatively short 
periods : the shortest known is /x^ Scorpii, only 35 hours. Beta Aurigae 
is a remarkable star of this 
class, the doubling of its 
lines taking place on alter- 
nate nights, giving a period 
of four days ; and the com- 
bined mass of both stars I889. Dec 30 d 17.6 h.. G M T. .single; 

is more than twice that 
of the sun. The region of 
its spectrum is here shown, 
with lines both double and 
single. New stars of this 
type are continually com- 1889, Dec. 31 d 11.5 h., g.m.t. (double) 

ing to light ; but if the or- Spectra of ^ Aurigae (Pickering) 

bits lie perpendicular to the 

line of sight, the duplicity is not discoverable in this manner. The one 
first found by E. C. Pickering in 1889 is perhaps the most remarkable 
of all ; it is Zeta Urs^ Majoris (Mizar), the A" line in whose spectrum 
becomes periodically double, indicating a period of about 52 days. The 
measured distance of the double lines gives a relative velocity of 100 
miles per second, and the mass of the system exceeds that of the sun 
forty fold. Belopolsky's recent investigations with the great Pulkowa 
refractor, prove that a^ Geminorum, one of the component stars of Cas- 
tor, also is a swift moving spectroscopic binary. 

Multiple stars. — Numerous stars have more than two 






1 



456 Stars and Cosmogony 

components in the same field of view. These are gener- 
ally called midtiple stars, though the terms triple star for 
three components, qitadriLple for four, and so on, are often 
used. In isolated instances a star may be optically mul- 
tiple; that is, the components appear to be associated 
together, from the fact that they are in or near the line of 
sight, while in reality they are at vastly different distances 
from the sun, and are in no sense related to each other. 
Nearly all multiple stars are physically multiple ; that is, 
connected together in a real system. Such a system is the 
star Epsilon Lyrae, the well-known fourth-magnitude star, 
near Vega. A keen eye, even without optical assistance, 
will split it into a double. A small telescope will divide 
each of the two components into a pair, forming a beau- 
tiful quadruple system; while large telescopes show at 
least three other faint stars, one of them very difficult, 
between the pairs. Not only do the two stars of each pair 
revolve round each other, in periods of several hundred 
years, but the pairs themselves have a grander orbital mo- 
tion round each other in a vast period not yet determined. 
A multiple star having more than seven or eight compo- 
nents would be classed as a star cluster. 

Stellar Clusters. — Seeming aggregations of stars in the 
sky are called stellar clusters, or simply clusters. Broadly 
speaking, they are embraced in two classes : The loose 
clusters, so called because the stars are not very thickly 
scattered, of which the Pleiades are a very conspicuous 
type ; and the close clusters, in which the stars appear to 
be thickly aggregated. The Pleiades contain six stars vis- 
ible to the ordinary naked eye, though seven, nine, and even 
as many as thirteen stars have in rare instances been seen 
in this group without a telescope. A medium glass shows 
about 100 stars, and a photographic plate exposed an 
hour displays more than 2000 stars in and close to the 



Stellar Clusters 457 

Pleiades. An exposure of six hours shows 4000 stars. 
The longer the exposure, the more stars appear on the 
plate. By an exposure of 17 h. 30 m., continued on nine 
nights, and covering a region of four square degrees, 
nearly 7000 stars are counted in the Pleiades. Recent 
counts make them fewer in the immediate regions of the 
bright stars than in adjacent portions of the sky of equal 
area ; and very much fewer than in many parts of the 
Milky Way. Also by photography Barnard has discov- 
ered extensive nebulosities surrounding the Pleiades, which 
the glare of the larger stars makes difficult to see with a 
telescope. They have crudely the shape of a horseshoe. 

One type of close clusters is known as the globular cluster^ in which 
the stars are compacted together as if in a seemingly circular area, 
or in space a nearly globular 
mass. The adjacent picture 
is an excellent illustration of 
this type. The more nearly 
spherical a cluster is, the older 
it is thought to be ; for the in- 
dividual components of clus- 
ters are no doubt subject to the 
laws of central attraction, and 
the more perfect approach to 
a spherical figure would indi- 
cate that the action of central 
forces had been longer con- 
tinued. Thus it is possible 
to infer the maturity of a 
cluster from the relative dis- 
position of its component Globular Cluster 15 Pegasi (Roberts) 
numbers. One of the finest 

objects in the sky is the double cluster, excellently reproduced in the 
next photograph. It forms part of the Milky Way in Perseus, and each 
component approaches the globular form. The clusters are made up of 
stars of all sizes, and are without doubt at stellar distances from us, 
though no parallax of a cluster has yet been measured. In all, about 
200 clusters and nebulae have been photographed, so that a half century 
hence it may be possible to ascertain what changes are taking place. 




458 



Stars and Cosmogony 



The Galaxy, or Milky Way. — Lying diagonally across 
the dome of the sky, at varying angles and elevations in 
different seasons of the year, may be seen on clear, moon- 
less nights an irregular belt or zone of hazy light of uneven 




The Double Cluster in Perseus (photographed by Roberts) 

brightness, about three times the breadth of the moon, 
and stretching from horizon to horizon. This is part of 
the Galaxy, or Milky Way. It is really a ring of light, 
reaching entirely round the celestial sphere, roughly in a 
great circle ; and usually about half of it will be above the 
horizon and half below. It intersects the ecliptic near the 
solstices, at an angle of about 60°. Early in September 



Stellar Distribution 459 

evenings it nearly coincides with a vertical circle lying 
northeast and southwest. The Galaxy is fixed in relation 
to the stars, and part of it lies so near the south pole of 
the heavens that it can never be seen in our northern 
latitudes. From Cygnus to Scorpio it is a divided belt, or 
double stream. Even a small telescope shows at once 
that the Milky Way is composed of millions of faint stars, 
nearly every one of them individually too faint for naked- 
eye vision, but whose vast numbers give us collectively 
the gauzy impression of the Galaxy. On page 13 is an 
excellent reproduction from one of the finest of Barnard's 
photographs of the Milky Way, and equally striking photo- 
graphs have been obtained by Wolf, and of the Southern 
Milky Way by Russell. All these stars are suns, and 
probably comparable in size and constitution with the 
sun himself. 

They are not evenly scattered, but in many regions are aggregated 
into close clusters of stars ; for example, the double cluster in the sword 
hilt of Perseus, shown opposite. It is readily visible to the naked eye 
on clear, moonless nights in the position shown in diagram on page 66. 
According to Easton, the galactic system accessible to our observation 
has but little depth in proportion to its diameter. Study of the photo- 
graphs has led Maunder to direct attention to 'dark lanes ' in the Milky 
Way, marking regions of real barrenness of stellar material, and per- 
haps indicant of galactic condensation progressing toward an ultimate 
globular cluster. 

Distribution of the Stars. — As to their apparent dis- 
tribution over the face of the sky, lack of uniformity is 
evident. The fact of their recognized division into con- 
stellations, even from the earliest ages, is proof of this. 
Clusters and starless vacuities are well known. Frequently 
there are found streams of stars, especially by exploration 
with the telescope. One general law is known to govern 
the apparent distribution in the heavens : at both poles of 
the Milky Way, the stars are scattered most sparsely ; 



460 



Stars and Cosmogony 



and the number in a unit of surface of the stellar sphere 
increases on all sides uniformly toward the plane of the 
Milky Way itself. This important discovery was made by Sir 
William Herschel, through a laborious process of actually 
counting the stars, technically called * star gauges.' In 
Coma Berenices, for example, near the north pole of the 
Milky Way, are perhaps five stars in a given area; half 
way to the Galaxy the number has doubled; and in the 
Milky Way itself the average number is found to exceed 
120, thus increasing more rapidly as this basal plane of 
the sidereal universe is approached. Kapteyn, a recent 
investigator of this supreme problem, likens the general 
shape of the stellar universe to that of the great nebula in 
Andromeda (opposite); the disk-shaped nucleus represent- 
ing the cluster to which the sun belongs, and its exterior 
rings the flattened layers of stars surrounded by the zone 
of the Galaxy. 

The Nebulae. — A nebula is a celestial object, often of 
irregular form and brightness, appearing like a mass of 

luminous fog. In all, 
about 8000 are now 
known, and their posi- 
tions among the stars 
determined. They differ 
greatly in brightness, 
form, and apparent size. 
Many of them are shown 
by the spectroscope to 
be glowing, incandescent 
gases, in large part hy- 
drogen. These are green- 
ish in tint; but a few 

Ring Nebula in Lyra (Roberts) -, ... 1 ^^^ *.^^^l,r 

^ ^ whitish ones are resolv- 

able; that is, composed of masses of separate stars too 




Rema7'kable Nebulce 



461 



faint to be seen individually. The nebulae appear like the 
residue of the materials of original chaos out of which the 
sun, his planets, and the stars have through many millions 
of years come into being. A few of them are variable in 
brightness. 

Classification of the Nebulae. — It is usual to divide the 
nebulae into five classes, based on their various forms : 
(i) annular nebulae, (2) spiral nebulae, (3) planetary nebulae, 
(4) nebulous stars, (5) irregular nebulae, for the most part 
large. A sixth class, elliptic nebulae, is sometimes recog- 
nized; probably they are annular nebulae seen edgewise, or 
nearly so. But some of the so-called annular nebulae ap- 
pear elliptic also. Every degree of eccentricity in their 
figure is recognized — some are merely oval, others are 
drawn out (page 469) into a mere line. Swift has made 
numerous nebular discoveries, and the most extensive cata- 
logue of nebulae is by Dreyer. 

By prolonged exposures 
fine photographs of the fainter 
nebulae have been obtained 
by von Gothard and others. 
A famous nebula of the irreg- 
ular order surrounds the star 
Eta Argus (page 428). In 
recent years it has been fre- 
quently photographed by Gill 
and Russell with exposures of 
many hours' duration, and 
changes in its brightness are 
plainly indicated. 

Remarkable Annular and 
Elliptic Nebulae. — A fine ob- 
ject of this class was dis- 
covered by Gale in 1894 in 
the southern constellation 
Grus ; but the best-known 
annular nebula is in the con- 
stellation Lyra. A very faint object in small telescopes, the great ones 




The Great Nebula in Andromeda (Roberts) 



462 Stars and Cosmogony 

reveal many stars within its interior spaces. The illustration on p. 460 
is from a photograph of the nebula, but it does not show the complexity 
and irregularity of structure which some of the large telescopes indicate. 
The star near its center is thought to be variable. Among elliptic neb- 
ulae, the signal object is the * great nebula in Andromeda.' So bright is 
it that the unaided eye will recognize it, near Eta Andromedae. Its vast 
size, too, as seen in the telescope, is remarkable — about seven times 
the breadth of the moon, and its width more than half as great. The 
illustration shows its striking structure, first clearly revealed by Rob- 
erts's splendid photographs in 1888. Apparently it is composed of a 
number of partially distinct rings, with knots of condensing nebulosity, 
as if companion stars in the making. Its spectrum shows that it is not 
gaseous, still no telescope has yet proved competent to resolve it. 

Spiral and Planetary Nebulae. — The great reflecting tel- 
escope of Lord Rosse first brought to light the wonderful 

spiral nebulae, the most 
conspicuous example of 
which is found in Canes 
Venatici. Its structure 
is such that photography 
has a vast advantage in 
depicting it, as the ad- 
jacent illustration re- 
veals. The convolutions 
of the spiral are filled 
with many star-like con- 
densations, themselves 
surrounded by nebulos- 

Spiral Nebula in Canes Venatici (Roberts) ., rr^. 

ity. 1 he spectroscope 
indicates its stellar character, though, like the Andromeda 
nebula, it is yet unresolved, except in parts. Planetary 
nebulae have this name because they exhibit a disk with 
pretty definite outlines, round or nearly so, like the large 
planets, though very much fainter. They are nearly all 
gaseous in composition. Nebulous stars are stars com- 
pletely enveloped as if in hazy, nebulous fog. They are 




Great Nebtila in Orion 



463 



mostly telescopic objects, and very regular in form, some 
with nebulosity well defined, others less so. One has 
luminous rings surrounding it. 

Spectra of the Nebulae. — Sir William Huggins, who in 1864 first 
applied the spectroscope to nebulae, discovered bright hnes in their 
spectra, indicating a community of chemical composition, due to 
glowing gas, in large part hydrogen. Helium has recently been 
added ; but other lines are due to substances not yet recognized as ter- 
restrial elements. The annular, planetary, and mostly the irregular neb- 
ulae give the gaseous spectrum ; and exceedingly high temperatures are 
indicated, or else a state of strong electric excitement. Both tempera- 
ture and pressure appear to increase toward the nucleus of the nebula. 
Many nebulae fail to yield bright lines ; showing rather a continuous 
spectrum, prominently the great nebula of Andromeda. Lack of lines 
may be interpreted as due to gases under extreme pressure, or to ag- 
gregations of stellar bodies. Another object of this character is the 
great spiral nebula in Canes Venatici, well depicted in the photograph 
by Roberts (opposite) ; but no telescope has yet been able to resolve 
either of these objects into discrete stars. The application of photog- 
raphy has revealed about 40 hnes in the spectra of nebulae ; and Keeler 
and Campbell have shown, in the case of the Orion nebula, that nearly 
every line in its spectrum is the counterpart of a prominent dark line in 
the spectra of the brighter stars of the same constellation. 

The Great Nebula in 
Orion. — Just below the 
eastern end of Orion's 
belt is this greatest of all 
nebulae. So characteris- 
tically bright is this well- 
known object that it is 
readily distinguished 
without a telescope. It 
was : the first nebula 
ever photographed — by 
Henry ..Draper in 1880. 
The- -spreading expanse 
of its nebulosity completely envelopes the multiple star 




The Great Nebula in Orion i Roberts) 



464 



Stars and Cosmogony 



Theta Orionis, often called the 'trapezium' (not well shown 
in the photograph because the blur of the nebula overlaps 
it). In small instruments a very obvious feature is the 
wide opening at one side, or break in the general light, 
sometimes called the 'Fish's mouth.' A curdling or floc- 
culent structure is excellently shown in the best photo- 
graphs, and a greenish tinge has been recognized in its 
light. Extensive wisps of nebulosity reach out in many 
directions, involving other stars. W. H. Pickering's plates 
indicate an approach to the spiral figure in these outlying 
filaments, and Roberts's photographs show vortical areas 
within the nebula. Its spectrum reveals incandescent 
hydrogen and helium; also other substances not yet recog- 
nized among terrestrial elements. The nebula is as remote 




Path of Milky Way and Distribution of Nebulae (according to Proctor) 

as the stars are ; and, according to Keeler's observations, 
its distance from the sun is increasing at the rate of 1 1 
miles every second. Also they prove an intimacy of rela- 
tion between the nebula and neighboring stars. There is 
no conclusive evidence of change of form in any part of 
the nebula, although H olden has investigated this question 



The Cosmogony 465 

fully. He found, however, fluctuations of brightness in 
several regions, which Stone is now studying critically. 

Distribution of the Nebulae. — It may be said that the 
nebuke are distributed over the sky in just the opposite 
manner from the stars ; for their number has a definite 
relation to the Milky Way. Reference to the preceding 
figure will show this at a glance. The small dots rep- 
resent nebulae, not stars ; and it is at once evident that 
they are more strongly clustered the greater their angular 
distance from the Milky Way. The physical reason under- 
lying this fact is not known. Neither is the distance of 
any nebula known. So that the distribution of the nebulae 
throughout space can only be surmised. Measurement 
of the distance of a few nebulae has been attempted, with 
the disappointing outcome that their parallax is exceedingly 
small, and probably beyond our power ever to ascertain. 
They are, therefore, at distances from our solar system 
estimable in light years, like those of the stars. Keeler's 
spectroscopic observations prove that the nebulae are mov- 
ing in space at velocities comparable with those of the 
stars ; the bright nebula in Draco, for example, is coming 
toward the earth at the rate of 40 miles every second. 
None of the nebulae, however, have yet been discovered to 
partake of proper motion. 

The Cosmogony. — Cosmogony is the science of the 
development of the material universe. It has nothing to 
do with the origins of matter, and is concerned only with 
its laws and properties, and the transformations resulting 
from them. The ancient philosophers avoided the ques- 
tion of the origin of matter by asserting that the universe 
always had its present form from eternity ; many minds 
are still satisfied with a literal interpretation of the Gld 
Testament account of the creation, that the Almighty 
Power, out of nothing, built the universe in six days, sub- 
todd's astron. — 30 



466 



Stars mid Cosmogony 



stantially as observed in our own age ; according to the 
accepted cosmogony, the universe was in the beginning 
a widely diffused chaos, 'without form and void,' accord- 
ing to the Scriptures. Out of it has been evolved, by the 
long-continued action of fixed natural laws, the present 
orderly system of the universe. 

The Universe is exceedingly Old. — In outline, the ac- 
cepted cosmogony is this : Once in the inconceivably 
remote past, many hundreds of millions of years ago, 
all the matter now composing earth, sun, planets, and 
stars, was scattered very thinly through the untold vast- 
ness of the celestial spaces. The universe did not then 
exist, except potentially. Then, as now, every particle of 
matter attracted every other particle, according to the 
Newtonian law. Gradually centers of attraction formed, 
and these centers pulled in toward themselves other par- 
ticles. As a result of the inward falling of matter toward 
these centers, the collision of its particles, and their fric- 
tion upon each other, the material masses grew hotter and 
hotter. Nebulae seeming to fill the entire heavens were 

formed — luminous fire 
mist, like the filmy ob- 
jects still seen in the 
sky, though vaster, and 
exceedingly numerous. 

Stars and Suns from 
Nebulous Fire Mist. — 
Countless ages elapsed; 
the process went on, 
swifter in some regions 
of space than in others. 
Millions upon millions of nebular nuclei began to form ; 
condensation progressed ; because the particles could not 
fall directly toward their centers of attraction, vast nebular 




Ideal Genesis of Planetary System 
(Compare with actual nebula on page 461) 



Nebular Hypothesis 467 

whirlpools were set in motion ; axial rotation began ; and 
temperature rose inconceivably high at centers where 
condensation was greatest. The sun was one of these 
centers ; earth and all the other planets had not yet a 
separate existence, but the materials now composing them 
were diffused through the great solar nebula. Every star, 
whether lucid or telescopic, was such a center, or be- 
came one in the gradual evolution and process of world 
building. 

Planets from Nebulous Stars. — As contraction and con- 
densation went on, the whirling became swifter, because 
gravitation brought the particles nearer to the axis round 
which they turned, and there was no loss of rotational 
moment of momentum. Centrifugal force gave the whole 
rotating mass the figure, first of an orange, then of a vast 
thickened disk, shaped like a watch. Eventually the 
masses composing its rim could no longer whirl round 
as swiftly as the more compact central mass ; so a sepa- 
ration took place, the outlying nebulous regions being left 
or sloughed off as a ring, while all the central portion kept . 
on shrinking inward from it. As shown opposite, the mass 
of the ring would rarely be distributed uniformly ; but being 
lumpy, the more massive portions would in time draw in 
the less massive ones, and the ring would thus become a 
planet in embryo ; and its time of revolution round the 
sun would be that of the parent ring. If still nebulous, 
the planet would itself go through the stages of the solar 
nebula, and slough off rings to gather into moons or 
satellites. Meanwhile the parent nebula went on con- 
tracting, and leaving other rings, which in the lapse of 
ages developed into inner planets, and their rings as a rule 
into satellites. 

Early History of the Nebular Hypothesis. — Such in bare 
outline is the nebular hypothesis. Note that it is merely a 



468 Stars and Cosmogony 

highly plausible theory ; it has never been absolutely demon- 
strated, and probably never can be. To its development 
many great minds have contributed. The Englishman 
Thomas Wright, the Swede Emanuel Swedenborg, and the 
German Immanuel Kant, all, independently and during 
the 1 8th century, appear to have originated the hypothe- 
sis under slightly variant forms. Of these, Kant's theory 
was the most philosophic; but his greater renown as a 
mental philosopher than as a physicist appears to have 
hindered attention to his important speculation. When, 
however. La Place lent the gravity of his great name to 
an almost identical hypothesis, astronomers at once recog- 
nized that it must be based on sound dynamic concep- 
tions. Then came the giant telescopes of the Herschels, 
father and son, and of Lord Rosse, adding the evidence of 
observation ; for they discovered in the sky nebulae, some 
globular in figure, some disk-like, others annular, and still 
others even spiral. 

Later Developments. — But Lord Rosse's great telescope 
showed, too, that some at least of the nebulae might be re- 
solved into stars, thereby threatening the subversion of 
the nebular hypothesis, especially if all the nebulae could 
be so resolved. Within a few years, however, and just 
after the middle of the 19th century, application of the 
principles of spectrum analysis to the nebulae proved 
conclusively that many of them are composed of glowing 
gas, and therefore cannot be resolved into stars. About 
the same time von Helmholtz advanced the accepted theory 
of the sun's contraction in explanation of the maintenance 
of solar heat ; and Lane, an American, proved that a 
gaseous mass condensing as a result of gravitation might 
actually grow hotter, in spite of its immense losses of heat. 
Thus it was unnecessary to assume a high temperature of 
the nebula in the beginning. Also the genius of Lord 



Darwin and See 



469 



Kelvin, the eminent English physicist, strengthened the 
hypothesis by computations on the heat of the sun, and 
his probable duration of about 20,000,000 years in the 
past. 

Recent Additions. — Then came Darwin, who, in the 
latter part of the 19th century, demonstrated mathemati- 
cally the remarkable effects producible by tidal friction, 
which had been neglected in all previous researches. The 
gathering of a ring into an embryo planet was a process 
not easy to explain ; and Darwin showed that probably 
the moon had never been a ring round the earth, but that 
she separated from her parent in a globular mass, in con- 
sequence of its too rapid whirling. He showed, too, how 
the mutual action of great tides in the two plastic masses 
would operate to push the moon away to her present re- 
mote distance : the terrestrial tidal wave being in advance 
of the moon, our satellite would tend to draw it backward ; 
also, the wave would tend to pull the moon forward, thereby 
expanding her orbit, and increasing her mean distance from 
us. His researches cleared up, also, the enigma of the 
inner satellite of Mars, revolving round its primary in less 
time than Mars himself turns on his axis ; and no less the 
newly discovered fact 
that Mercury and Venus 
keep a constant face to 
the sun, and satellites of 
Jupiter to their primary, 
just as the moon to the 
parent earth. Still later, 
by adapting these prin- 
ciples to stellar systems. 
See explained the fact of 
the great eccentricity of 
the binary orbits as a result of the long-continued or secu- 



1 


1=1 




IV 


V 





Various Types of Double Nebulae (Lord Rosse) 



470 Stars and Cosmogony 

lar action of tidal friction. The double stars, then, were 
originally double nebulae, separated by a process resem- 
bling ' fission ' in the case of protozoans. Poincare has 
proved mathematically that a whirling nebula, in conse- 
quence of contraction, is liable to distortion into a pear- 
shaped or hour-glass figure, and to ultimate separation. 
And there is excellent observational proof in the double 
nebulae (p. 469) found in different regions of the heavens. 

Evidence supporting the Nebular Hypothesis. — To collect 
evidence from the entire universe, as at present known : — 

(a) Scanning the heavens with the telescope, we find 
numerous nebulae of forms required by the theory. 

{b) Spectrum analysis proves a general unity of chemical 
composition throughout the universe. 

{c) Stellar evolution necessitates the supposition of birth, 
growth, and decay of stars, — a requirement met by the fact 
that types of stellar spectra differ greatly, possibly indica- 
ting a wide variation in age of the stars, although this is 
not yet clearly made out in all detail. 

{d) Our sun is a star, and its corona resembles such 
wisps of nebulous light as theory would lead us to expect. 

{e) The maintenance of solar heat is best explained on 
the basis of the sun's continual contraction. 

(/) The planets revolve round the sun, and the satellites 
round the planets, in nearly the same plane (with few ex- 
ceptions not difficult to account for). 

(^g) The planets all rotate on their axes (so far as 
known), also revolve in their orbits round the sun, in the 
same direction. 

(//) The zone of small planets circling about the sun, 
and the triple ring surrounding the planet Saturn, are 
eminently suggestive and seemingly permanent illustra- 
tions of a single stage of the interrupted process of world 
building in accordance with the nebular hypothesis. 



Other Universes 471 

Other Universes than Ours. — When considering known 
stellar distances, we found stars immensely remote from 
the solar system in all directions ; and everywhere scat- 
tered among myriads remoter still, whose distances we can 
see no prospect of ever ascertaining. What is beyond ? 
Outside the realm of fact, imagination alone can answer. 
We cannot think of space except as unlimited. The con- 
cept of infinite space precludes all possibility of a boun- 
dary. But the number of stars visible with our largest 
telescopes is far from infinite ; for we should greatly over- 
estimate their number in allowing but ten stars to every 
human being alive this moment upon our little planet. 
Are, then, the inconceivable vastnesses of space tenanted 
with other universes than the one our telescopes unfold } 
We are driven to conclude that in all probability they are. 
Just as our planetary system is everywhere surrounded by 
a roomy, starless void, so doubtless our huge sidereal clus- 
ter rests deep in an outer space everywhere enveloping 
inimitably. So remote must be these external galaxies 
that unextinguished light from them, although it speeds 
eight times round the earth in a single second, cannot 
reach us in millions of years. Verily, infinite space tran- 
scends apprehension by finite intelligence. Let us end 
with Newton, as we began. * Since his day,' wrote one 
, of England's greatest astronomers in his Cardiff address 
(1891), 'our knowledge of the phenomena of Nature has 
wonderfully increased; but man asks, perhaps more 
earnestly now than then, what is the ultimate reality 
behind the reality of the perceptions } Are they only the 
pebbles of the beach with which we have been playing } 
Does not the ocean of ultimate reality and truth lie 
beyond ? ' 



INDEX 



Abbe, E., Dir. Obs. Univ. Jena 199 
Aberration, annual 162, constant of 163, 

ellipses 164, 437, stellar 164 
Aberration time 329 
Achernar (a Eridani) 423 
Actinometer 194 

Adams, J. C. (1819-92), Eng. ast. 369, 370 
Agathocles (b.c. 320), eclipse of 289 
Alaska transferred to U. S. 188 
Albategnius, M. J. (a d. 900), Arab. ast. 247 
Aldeb'aran, Plate iv. 62, 423, 434, 439, 441 
d'Alembert, J. B. le R. (da-long-ber') (1717- 

83), Fr. math. 247 
Alexander, S. (1806-83), Am. ast. 296 
Algol, Plate III. 60, 441, 446, 450 
Almagest of Ptolemy 313 
Al-Mamun (a.d. 810), Arab, caliph 80 
Almanac, Naiitical 112, 170 
Almucantar defined 28 
Alpheratz (a Andromedse) 66 
Altair, Plate iv. 62, 423, 434, 439, 441, 445 
Altazimuth 48, 81 

Altitude, defined 47, 58, measuring 181 
Amherst College, lunar eclipse at 308, mete- 
orite collection 412, 418, 419 
Anaximan'der (b.c. 580), Gk phil. 23, 76 
Andromeda, Plate iii. 60, Plate iv. 62, nebula 

in 462, new star in 447 
Andromedes, meteors 403, 414, 417 
Angle of the vertical 87 
Angles, instruments for measurmg 193, 208, 

measure of 44, relation to distance 45 
Anta'res (a Scorpii) , Plate iv. 62, 423, 425, 442 
Apastron defined 453 
Aphelion defined 139 
Apogee, moon's 233 
Ap'sides, line of, defined 139 
Aquarids, Delta, Eta, meteors 414 
Aquarius, Plate iv. 62 
Aquila, Plate iv. 62 
Archime'des (b.c. 250) Gk. geom. 247 
Arcturus, Plate iv. 62, 423, 439, 441, 444 
Argelander, F. W. A. (1799-1875), Ger. ast. 

424, 425 
Argo, Plate iv. 62 
Argus, Eta, nebula 428, 449, 461 
Ariel, satellite of Uranus 347 
Aries, Plate iv. 62, First of 38, 109 
Aristarchus (b.c. 270), Gk. ast. 247 
Aristotle (b.c. 350) Gk. phil 80, 247 
d'Arlandes, F. L. (dar-lond') (1742-1809), 

Fr. marquis 291 
Arzachel, A. (ad. 1080), Heb. ast. 247 
Assyria, chronology of 8, tablets 289 
Asteroids 314, 335, 361, 362 
Astrographic charts 427 
Astrolabe, ecliptic 57 
Astronomer Royal 433 
Astronomy, before telescopes 190, defined 7, 

history 7, 43, 57, 76, 80, 81, 97, 114, 129-31, 

166, 190, 199, 203, language of 22, practical 

defined 43, utility of 8 



Atmosphere, of earth 90-4, of moon 243, of 

stars 426, of sun 279, steady 191 
Auriga, Plate iii. 60, Plate iv. 62, 447-9 
Aurigae, Beta 455 
Aurora 94, spectrum 94 
Autumn in general 153, months of 159 
Auwers, A. (ow'verz), Ger. ast. 261,430 
Axis, optical 195 
Azimuth defined 47, 58 



Bache, A. D. (bach) (1806-67), Am. physicist 

444 
Bailey, S. I., Am. ast. 428, 446 
Ball, Sir R. S., Dir. C)bs. Cambridge, Eng. 

64, 440 
Barnard, E. E., Prof. Univ. Chicago, 4, 13, 18, 

33. 34, 307, 335, 344, 352, 357, 393, 401, 405, 

406, 408, 411, 457, 459 
Bede (bead) ' The Venerable ' (a.d. 700), Eng. 

author 76 
Beer, W. (bay'er) (1797-1850), Ger. banker 

and ast. 355 
Belopolsky, A., ast. Pulkowa Obs, 455 
Berliner Astron. Jahrbtich 362 
Bessel, F. W. (1784-1846), Ger. ast. 437, 

454 
Betelgeux (bet-el-gerz') Plate iv. 62, 423, 

425, 434 
V. Biela, W. (be'la) (1782-1856), Aus. officer 

401, 403, 411, 418 
Bielids (be'lidz), meteors 403, 418 
Bigelow, F. H., U. S. Weather Bureau 300 
Bigourdan, G. (be-goor-dong), ast. Pans Obs. 
„.452 
Bmary stars 452, eccentricities 453, masses 

453, spectroscopic 454 
Bisch'offsheim, R., Fr. banker and patron 202 
Blanpain, M. (1779-1843), Fr. ast. 401 
Bode, J. E. (bo'duh) (1747-1826), Ger. ast., 

law of 333, 361 
Bolometer 194, 277 

Bond, G. P. (1825-65), Am. ast. 368, 452 
Bond, W. C. (1789-1859) Am. ast. 346 
Bootes, Plate in. 60, Plate iv. 62 
Boss, L., Dir. Dudley Obs. 427, 431 
Box-transit 118 
Boyden, U. A. (1804-79), Am. engineer and 

patron 192, 444 
Brachy-telescope 204 
Bradley, J. (1693-1762), Ast. Royal 163 
Brashear, J. A. 191, 203, 205, 272, 281 
Bredichin, T. (bray-de-kang ), Russ. ast. 396 
Brenner, L., ast. (3bs. Lussinpicolo 369, 370 
British Museum meteorites 412, 419 
Brooks, W. R., Dir. Obs. Geneva 393, 401, 

405, 406, 41 T 

Brorsen, T. (1819-93), Ger. ast. 351, 393 
Bruce, Miss C. W., Am. patron 429 
Bruce telescope 14, 428 

Btilletin Astronomique (Paris monthly) 284 
Burnham, S. W., Univ. Chicago 451, 453 



473 



474 



Index 



Caesar, Julius, reforms calendar i66 

Calcium in sun 270, 276 

Calendar, 165, reform of 166, 167 

Calorie defined 286 

Camelopardalis, Plate iii. 60 

Campbell, W. W., ast. Lick Obs. 349, 434, 

443. 463 

Canals of Mars 358 

Cancer, Plate iv. 62, tropic of 160 

Canes Venatici, Plate iii. 60, Plate iv. 62, 
nebula in 462 

Canis major, Plate iv. 62 

Canis minor, Plate iv. 62 

Cano'pus (a Argus) 423, 431 

Cape of Good Hope, Obs. 427, 437, tide 177 

Capella, Plate in. 60, 423, 425, 439, 441, 442 

Capricornus, Plate iv. 62, tropic of 160 

Carbon, in comets 406, in stars 443, in sun 276 

Cardinal, directions in sky 41, points 23 

Carina, Plate iv. 62, new star in 448 

Carina, Eta, 428, spectra 444 

Cassegrainian telescope 203 

Cassini, G. D. (kas-se'ne) (1625-1712), It.-Fr. 
ast. 346, 357, 364, 368 

Cassiopeia, Plate 111. 60, 116, 430, 447 

Castor (a Geminorum), Plate iv. 62, 452, 455 

Centauri, Alpha 20, 423, 439, 453 

Centaurus, Plate iv. 62, new star in 448 

Central sun hypothesis 431 

Cepheus (se'fuce), Plate in. 60 

Ceres, first small planet discovered 361 

Cetus, Plate iv. 62 

Chaldean view of comets 392 

Chandler, S. C, ed. Astron. Jotir. 96, 446 

Charles II (1630-85), Eng. king 433 

Charlois, ]\I. (shar-lwah'), ast. Nice Obs. 362 

Chinese annals 289, 447 

Chlorine, in comets 396, not in sun 277 

Christie, W. H. M., Ast. Royal 4, 433 

Chromosphere, solar 280, 284 

Chronograph 193, 213, printing 214 

Chronology 8 

Chronometer, marine 170-3, 193 

Circle, graduated 193, great, defined 28, sub- 
division of 43, vertical, defined 28 

Clark, A. (1804-87), A. G. (1832-97), G. B. 
(1827-91), 15, 191, 202, 203, 360, 453 

Clarke, J. F. (1810-88) Am. theol. 63 

Clavius, C. (1537-1612), Ger. math. 247 

Cleome'des (a.d. 150), Gk. ast. 80 

Clep'sydra, ancient 114 

Gierke, Miss A. M. (klark), Eng. ast. 442 

Clocks 193, 211, error of 211 

Clusters, globular 457, stellar 456 

Cobalt in sun 276 

Coggia, M. (ko'jha), ast. Obs. Marseilles 
404, 405 

Collimation, line of 210 

Collimator 271 

Columba, Plate iv. 62 

Colure', defined 35, 58, equinoctial 66 

Coma Bereni'ces, Plate iv. 62 

Comets 20, 392, appearance 394, changes 395, 
chemical composition 406, collision with 409, 
coma 394, connection with meteors 417, con- 
stitution 396, density 408, dimensions 399, 
direction of motion 399, discoveries 393, 407, 
disintegration of 403, 410, Donati's 20, 393, 
394, 404, earth passes through 409, families 
400, form 394, 395, greatest 403, groups 400, 
head 394, light 406, mass 408, motion 399, 



next to come 405, now due 406, nucleus 394, 
number 402, observations 397, orbits 397, 
origin 410, periodic 399, photography of 407, 
remarkable 402-5, superstitions 392, tails 
394-6, tandem 400, 411, velocity 398 

Common, A. A., Eng. ast. 205, 365 

Comparison prism 275 

Comstock, G. C, Dir. Obs. Univ. Wis. 244, 

Conjunction, moon's 232, planets' 315, 317, 

in right ascension 318 
Constellations 14, 59-64, 430 
Contacts, in eclipses 298, in transits 340 
Copernicus, N. (1473-1543), Ger. ast. 97, 247, 

251J 252, 313, 392 
Copper in sun 276 

Cornu, A., Ecole Poly tech., Paris 143, 279 
Coro'na 285, 290, 299, periodicity 301, rotation 

300, 303, spectrum 300, 302, streamers 301 
Corona Australis, Plate iv. 62 
Corona Borealis, Plate iv. 62, nova 447 
Coronium 300, 302 
Corvus, Plate iv. 62 

Cosmas (a.d 550), Egyp. geographer 76 
Cosmogony 421, 465-70 
Cotidal lines 177 

Coude (coo-day'), equatorial 217 
Crater, Plate iv. 62, lunar 247 
Crew, H., Prof. Northwestern Univ. 270 
Cygni 61, 437,439, 452 
Cygnus, Plate iii. 60, nova of 1876 in 447 

Daguerre, L. J. M. (da ger') (1789-1851), Fr. 
painter 218 

D'Arrest, H. L. (dar-rest') (1822-75), Ger. 
ast. 401 

Darwin, G. H., Prof. Univ. Cambridge, Eng. 
338, 469 

Day {see Night) 100, apparent solar no, as- 
tronomical III, change of 187, civil in, 
length of 106, mean solar no, sidereal 108, 
sidereal and solar compared 145 

Declination, defined 50, 58, parallels of 35 

Declination, axis 53, circle 53 

Decrescent moon 225 

Deferent circle defined 312 

Delphinus, Plate iv. 62, variable in 449 

Dembowski, L. (1815-85), Ger. ast. 451 

Deneb (a Cygni), Plate iii. 60, 423 

Denning, W. F., Eng. ast. 364, 401. 414 

Deslandres, H. (day-londr'), ast. Paris Obs. 
282, 300, 301, 445 

De Vico, F. (1805-48), Ital. ast. 401 

Diamond in meteorites 419 

Diffraction, grating 273, rings 201 

Di'o-ne, satellite of Saturn 346 

Dip of the horizon 183 

Dipper 60, Plate in., 116, 430 

Directrix of parabola 398 

Disk of planets 18, 318, 331 

Distances, celestial, moon 233, 236, planets 
325, 327, 333. stars 435-40, sun 143, -257 

Diurnal, arc 30, motion 30 

Doerfel, G. S. (1643-88), Ger. ast. 247 

Dollond, J. (1706-61), Eng. opt. 199 

Dona'ti, G. B (1826-73), Ital. ast. 393 

Donati's comet (of 1858) 20, 394, 396, 399, 
404 

Doolittle, C. L., Dir. Obs. Univ. Penn. 86, 96 

Doppler, C. (1803-53), Ger. physicist 432 

Doppler's principle 277, 279, 432, 455 



Index 



475 



Double stars {see Binary stars) 451, 452, bina- 
ries 452, colored 425, optical doubles 451, 
orbits of 453, origin of 469 

Douglass, A. E., Lowell Obs. 346, 352 

Draco, Plate in. 60 

Draconis, Alpha 130 

Draper catalogue, star spectra 444 

Draper, H. (1837-82), Am. ast. 205, 407, 444, 
463; Mrs. H. 444 

Dreyer, J. L. E., Dir. Obs. Armagh 461 

Duner, N. C, Dir. Obs. Upsala 270 

Earth, affected by sun spots 269, ancient idea 
of 76, atmosphere 90-4, axis moving in space 
130, curvature of 77, 78, direction of motion 
in space 134, form found by pendulums 88, 
mass 89, measurement 79. motion in orbit 
140, 144, oblateness 82, orbit an ellipse 136, 
orbit in future 139, path in space 431, proof 
of earth's motion 165, revolves round the 
sun 131, size 81, size of orbit 143, turns on 
its axis 97, 98, uniformity of rotation 126, 
volume 81, why it does not fall into sun 382 

Earthquakes and moon 245 

Easter Sunday 168 

Eastman, J. R., Prof. U. S. Navy 215 

Easton, C, Dutch ast. 459 

Eclipse seasons 309 

Eclipses (lunar) 305, dates of 307, 308, fre- 
quency 308, moon visible during 307, phe- 
nomena 307, recurrence 309, (solar) 233, 

289, ancient 289, annular 292, 296, cause of 

290, dates of 296, 302-4, frequency 308, fu- 
ture 304, life history of 310, near at hand 
303, number in year 294, partial 292, 295, 
phenomena of 297, prediction of 21, 304, 309, 
recurrence 309, toidX, /rofitispiece , 292, 297 

Eclipses of Jupiter's satellites 345 

Ecliptic, 55, 58, Plate iv. 62, 132, apparent 

motion 39, north polar distance 56, obliquity 

150, origin 293 
Ecliptic limit (lunar) 306, (solar) 294 
Ecliptic system, circles of 28, 36, glides over 

horizon system 38, origin of 55 
Edgecomb, W. C, Am. opt. 205 
Elkin, W. L., Dir. Yale Obs. 362, 411, 437 
Ellery, R. L. J., Govt, ast., Melbourne 208 
Ellipse, defined 136, eccentricity 137, how to 

draw 138, limits of 137, 397, parallactic 436 
Enceladus, satellite of Saturn 346 
Encke, J. F. (eng'kuh) (1791-1865), Ger. ast. 

396, 400, 401, 403 
Ephemeris 120, 123, 345 
Epicycle defined 312 
Equation of time 112, explained 150 
Equator, Plate iv. 62, celestial defined 35, 58, 

terrestrial, motion of stars at 72 
Equator system, circles of 28, 34, 58, glides 

over horizon system 36, origin of 50 
Equatorial girdle of stars, Plate iv. 62-3 
Equatorial telescope 52, 55, 192, adjusting 54, 

mounted at equator 74, at poles 73 
Equinoctial defined 50 
Equinoxes 37, defined 38, double use of term 

148, how to find 66, motion of 128, position 

of 130, precession 128, 390, 426 
Eratos'thenes (b.c. 240), Alex. geom. 80 
Er[icsson, J. (1803-89), Swed.-Am. eng. 286 
Eridanus, Plate iv. 62 
Escapements, clock 212 
Ether, luminiferous defined 44, 142 



Euclid (B.C. 280) Gk. geom. 43, 50 
Eudoxus (B.C. 370), Gk. ast. 59, 247 
Everett, Miss A., Eng. ast. 452 
Evolution, tidal 338, 469 
Eyepiece 195, negative 206, positive 207 

Faculae, solar 264, 269, 270 

Fargis, J. A., Prof. Georgetown Col. 215 

Faye, H. A. E. A. (fy), Pres. Bureau des 

Longitudes, Paris 401 
FerneljJ. (fair-nel') (1497-1558), Fr. geod. 80 
Finlay, W. H., ast. Capetown Obs. 401 
Flammarion, C. (flam-ma're-ong'), Dir. Ju- 

visy Obs. (Paris) 65, 179 
Flamsteed, J. (1646-1719), Ast. Roy. 247 
Fleming, Mrs. IVL, Am. ast. 444, 448 
Fomalhaut (fo'mal-6), Plate iv. 62, 423 
Fornax, Plate iv. 62 
Foucault, J. B. L. (foo-ko') (1819-68), Fr. 

physicist 99 
Fracastor, J. (1483-1553), It. physician 247 
v. Fraunhofer, J. ( frown 'ho-fer) (1787-1826), 

Ger. opt. 191, 443 
Fraunhofer lines 271, 275, 277, 279, 284 
Frost, E. B., Dir. Dartmouth Col. Obs. 286, 

445 

Gale, W. F., Australian ast. 407, 408, 461 

Galile'o, G. (1564-1642), It. ast. 14, 190, 196, 

^ 318, 344, 371 

Gases, kinetic theory of 244 

Gassendi, P. (1592-1655), Fr. ast. 247, 341 

Gegenschein (gay 'gen-shine) 315, 351 

Gemini, Plate iv. 62 

Geminids, meteors 414 

Geminus (b.c. 50), Gk. ast. 247 

Geodesy 9, defined 80 

Gill, D., Her Majesty's ast., Capetown 362, 

427, 437. 461 
Gimbals of chronometer 171 
Glasenapp, S. P. (glaz'nap), Dir. Obs. Saint 

Petersburg Univ. 452 
Glass, optical 196, new 199, 220 
Gnomon 23, 80, 114 
Goal, sun's 431 

v. Gothard, E. (go'tar), Dir. Obs. Hereny 461 
Gould, B. A. (1824-96), Am. ast. 424, 452, 457 
Graham, T. (graim) (1805-69) , Scot. chem. 420 
Gravitation 21, argument for universal 371, 

explains tides 387, holds moon and planets in 

orbit 376, law of 329, 380, 454, what it is 384 
Gravity, common center of 379, distinct from 

gravitation 384, terrestrial 87 
Great Bear 60, Plate 111. 61 
Great Circle courses 189 
Greek alphabet 60 
Green, N. E., Eng. ast. 355 
Greenwich, meridian of 123, in navigation 183, 

observatory 202, 366, 432-4 
Greenwich time, carried by chronometers 171 
Gregory, J. (1638-75), Scot. math. 203; R. A., 

Eng. ast. 440; XIII. reforms calendar 166 
Grimaldi, F. M. (1618-63), It. physician 247 
Groombridge, S. (1755-1832), Eng. ast. 430 
Grubb, Sir H., Brit. opt. 202; T. (1800-78). 

Brit. opt. 205 

Hadley, J. (1682-1744), Eng. math. 181 
Hale, G. E., Dir. Obs. Univ Chicago 4. 7 269 

281-3 
Hall, A., Prof. U. S. Navy (ret.) 343, 452 



476 



Index 



Hall, A., Jr., Dir. Obs. Univ. Mich. 385; 

C. M. (1703-71), Eng. math. 199 
Halley, E. (1656-1722), Ast. Roy. 394, 400, 

402, 405, 449 
Hamilton, Sir W. R. (1805-65), Brit. math. 7 
Hansen, P. A. (1795-1874), Ger. ast. 150 
Harkness, W., ast. Dir. U. S. Naval Obs. 302 
Harvard College, meteorite collection 412, 

Obs. 6, 14, 205, 422, 429, 444, 448, 449 
Hastings, C. S., Prof. Yale Univ. 191, 199 
Heat, lunar 245, sun's greatest at midday 155, 

at summer solstice 157, solar 286, 468 
Heliometer 193, 261, 437 
Helium 280, in meteorites 420, in nebulae 463, 

in stars 445 
V. Helmholtz, H. L. F. (1821-94), Ger. phys- 
icist 287, 468 
Henderson, A., Eng. ast. 365 
Henry, A. J., U. S. Weather Bureau 10 
Henry, P. and P. (ong-ree'), ast. Paris Obs. 

16, 202, 248 
Hercules, Plate in. 60, Plate iv. 62 
Herodotus (b.c. 460), Gk. hist. 76, 247 
Herschel, Miss C. L. (1750-1848), Eng. ast. 
393; Sir F. W. (1738-1822), Eng. ast. 204, 
205, 247, 347, 357, 369, 451, 460, 468; Sir 
J. F. W. (1792-1871), Eng. ast. 333, 409, 468 
Hesperia, on Mars, Plate vi. 360 
Hevelius, J. (1611-87), Ger. ast. 248, 269 
Higgs, G., Eng. physicist 276 
Hill, G. W., Pres. Am. Math. Soc. 221 
Himinel tind Erde (monthly) 6 
Hipparchus (b.c. 140), Gk. ast. 65, 129, 247, 

312, 426, 447 
Holden, E. S., Am. ast. 345 
Holmes, E., Eng. ast. 401 
Hori'zon, apparent 24, dip of 183, ocean, 25, 

rational 27, 58, sensible 25, visible 24 
Horizon system, circles of 28 
Horology 212 

Horrox, J. (1617-41), Eng. ast. 342 
Hough, G. W. (huff), Dir. Dearborn Obs. 

192, 214, 365 
Hour circle 35, 58, of telescope 53 
Huggins, Sir W., Eng. ast. 407, 434, 441, 463 
Hussey, W. J., ast. Lick Obs. 397, 407 
Huxley, T. H. (1825-95), Eng. biologist 2 
Huygens, C. (hy'genz) (1629-95), Dutch ast. 

190, 346, 354, 367, eyepiece 207 
Hydrocarbons, in comets 396 
Hydrogen, in earth's atmosphere 244, in 
moon's 244, in meteorites 420, in nebulae 
463, in stars 441, 445, 448, in sun 276, out- 
bursts in stars 451 
Hyperbola, comet orbit 397 
Hype'rion, satellite of Saturn 344, 346 

lapetus (e-ap'e-tus), satellite of Saturn 346 

Instruments classified 193 

Iron, in comets 396, 406, in sun 276 

James, A. C., D. W._, Am. patrons 2 

Janssen, P. J. C., Dir. Meudon Obs. 264 

Jena (yay'na) glass 199, 220 

Jeroboam II (b.c. 770), Assyrian monarch 8 

Jewell, L. E., Am. physicist 271, 276 

Juno, small planet 335 

Jupiter 17, albedo 333, atmosphere 349, belts 
363, center of gravity of sun and 336, chart 
of 365, color 332, configurations 317, density 
336, diameter 334, distance 328, drawings 17, 



363-5, eccentricity 324, ellipticity 337, family 
of comets 401, great red spot 364, libration 
338, loop of path 319, mass 335, naked-eye 
appearance 313, orbit 323, periods 325, 326, 
phase 319, photographs 365, relative dis- 
tance and motion 333, retrograde motion 320, 
rotation 336, 339, satellites 344-6, surface 363 

Kant, I. (kant) (1724-1804), Ger. phil. 468 
Kapteyn, J. C., Univ. Groningen, 429, 442, 

460 
Keeler, J. E , Dir. Allegheny Obs. 349, 350, 

363, 369, 434, 463, 465 _ 
Kelvin, Baron, Prof. Univ. Glasgow 469 
Kepler, J. (1571-1630), Ger. ast. 140, 247, 371, 

393, 429, 447, laws 326, 369, 375, 377-9, 385 
Kimball, A. L., Prof. Amherst Coll. 4 
Kirchhoff, G. R. (keerk'hoff ) (1824-87), Ger. 

physicist 191, 275 
Klein, H. J., Ger. ast. 64 
Knott, C. G., Lect. Edinburg Univ. 245 
Kranz, W. (kronts), Ger. painter, y'r^wz'. 

Lacaille, N. L. de (1713-62), Fr. ast. 440 

Lacerta, Plate iv. 62 

La Grange, J. L. (la-gronzh') (1736-1813), 
Fr. math. 139, 330 

Landreth, O. H., Prof. Union Coll. 216 

Lane, J. H. (1819-80), Am. physicist 468 

Langley, S. P., Sec. Smithsonian Institution 
245, 278, 279, 285, 348 

La Place, P. S. de (la-pl6ss') (1749-1827), 
Fr. ast. and math. 2, 330, 468 

Lassell, W. (1799-1880), Eng. ast. 205, 347 

Latitude (celestial) 55, 58, parallels of 37, pre- 
cession does not affect 130, (terrestrial) 
equals altitude of pole 69, finding 68, 82, 85, 
finding at sea 182, length of degrees 86, 
origin of term 76, variation of 95, 96 

Latitude-box 82 

Leavenworth, F. P., Prof. Univ. Minn. 452 

V. Leibnitz, G. W. (lib'nits) (1646-1716), Ger. 
math, and phil. 247, 250 

Lenses 195, 198, 200 

Leo, Plate iv. 62 

Leo Minor, Plate iv. 62 

Leonids, meteors 414, 415, 417 

Lepus, Plate iv. 62 

Le Verrier, U. J. J. (luh-vay-rya') (1811-77), 
Fr. ast. 150, 369, 370 

Lexell, W. (1740-84), Fr. math. 401 

Libra, Plate iv. 62 

Lick, J. (1796-1876), Am. patron, Obs. 192, 
211, 249, 359, 365, 407, 434, teles. 202, 424 

Light, moves in straight lines 44, velocity of 
142, 345, year, unit of distance 438 

Lindsay, Lord, Scot, noble and ast. 300 

Lockyer, Sir J. N., Eng. ast. 445, 451 

Loewy, M. (luh'vy), Dir. Paris Obs. 217 

Longitude (celestial) 56, 58, of stars changes 
by precession 130, (terrestrial) ascertaining 
by telegraph 123, at sea 182, defined 123, 
length of degrees of 86, origin of term 76 

Lovell, J. L , photographer, 116, 398 

Lowell observatory 192, 354 

Lowell, P., Am. ast. 352, 353, 358-60 

Lunation 230 

Lynx, Plate iv. 62 
I Lyra, Plate iv. 62, ring nebula in 460, 461 
: Lyrse, Beta 445, 446, Epsilon (ep-si'Ion), 456 
i Lyrids, meteors 4x4 



Index 



477 



V. Maedler, J. H. (med'ler) (1794-1874), Ger. 
ast. 355 . . ^ 

Magnesium, in comets 406, in sun 276 

Magnetic disturbances, 245, 268 

Magnifying power, 208 

Mantois, M. (man twa')) Fr. glass-maker 
15 

Mars, atmosphere 349, axial inclination 337, 
canals 359, color 332, configurations 317, 
density 335, diameter 334, distance 328, ec- 
centricity 324, ellipticity 337, libration 338, 
loop in path 319, markings on 358, mass 
335, 386, naked-eye appearance 313, oases 
359, oppositions of 356, orbit of 322, 355, 
periods 325, 326, phase 318, polar caps 349, 
357, relative distance and motion 333, retro- 
grade motion 320, rotation 337, 339, satel- 
lites 343, seasonal changes 360, surface of 
354, terminator 355, twilight arc 349, water 
on 355, variation in size 331 

Martin, T. H. (mar-tang'), Fr. opt, 202, 204 

Mascari, A., ast. Catania Obs. 353 

Maskelyne, N. (1732-1811), Ast. Royal 247 

Maunder, E. W., ast. Obs. Greenwich 434, 
440, 459 

Maury, Miss A. C., Am. ast. 444 

Mean noon, sidereal time of 121 

Mercury, albedo 332, atmosphere 348, color 
332, conjunctions 315, density 335, diame- 
ter 334, distance 328, eccentricity 324, great- 
est brilliancy 315, greatest elongation 316, 
inclination 324, libration 338, mass 335, 
naked-eye appearance 313, orbit 322, 
periods 325, 326, phase 318, relative dis- 
tance and motion 333, retrograde motion 
319, rotation 337, 339, surface of 352, tran- 
sits 339, 341 

Meridian 28, 58, arc 82, circle 86, 216, mark 
117, room 193 

Messier, C. (mes'se-a) (1730-1817), Fr. ast. 

393. 394 

Meteorites 20, 411, analysis 419, carbon in 
419, falls of 418, form irregular 419 

Meteoritic theory 451 

Meteors 20, 392, 411-417 

Meyer, M. W., Dir. Urania Gess. Berlin 6 

Michelson, A. A., Prof. Univ. Chicago 143 

Micrometer 193, 208 

Midnight sun 105 

Milky Way 13, described 458, lanes in 459 

Mimas, satellite of Saturn 346 

Mira 442, 445, 446 

Mizar, star in Ursa Major 117, 455 

Monoc'eros, Galaxy in 13, Plate iv. 62 

Montaigne, M. (mong-tayn') (1716-85), Fr. 
ast. 403 

Moon 16, 221, angular unit 46, apogee 233, 
apparent size 240, 241, aspects 232, atmos- 
phere 243, changes on 249, constitution 244, 

245, daily retardation 226, deviation 237, 
dimensions 238, distance 233, 236, earth- 
shine on 225, eclipses of 305, features of 

246, gravity at surface 242, harvest and 
hunter's 227, heat 245, illumination 223, 
224, librations 242, light 244, maps 248, 
mass 241, motion 221 (north and south), 
226, mountains on 249, 251, nodes 231, 293, 
orbit (apparent) 230, (inclination of) 231, 
(in space) 232, parallax 234, perigee 233, 
periods 228-9, phases 223, 224, photographs 
16, 248, rills 251, rotation 242, seas 246, 



streaks 251, temperature 245, visit to 253, 

water on 244, weather 245 
Moreux, T. (mo-ro'), Fr. ast. 11 
Motion, curvilinear 377, 381, defined 371, laws 

of 372-4, of stars in sight line 432, 434 
Mouchot, A. (moo-show'), Fr. phys 286 
Museums, astronomical 57 

Nadir defined 24 

Naples, Bay of 250 

Navigation 9, astronomy of 169, 433 

Nebulae 460, annular 461, classified 461, con- 
stitution 461-4, description 460, distance 
465, double 469, elliptic 461, Orion 463, 
planetary 443, 462, spectra 463, spiral 462 

Nebular hypothesis 465-70 

Neptune, albedo 333, atmosphere 350, Bode's 
law 333, color 332, configurations 317, den- 
sity 336, diameter 334, discovery of 369, 
379, distance 328, eccentricity 324, mass 
335, orbit 323, periods 325, 326, relative dis- 
tance and motion 333, retrograde motion 
320, rotation 337, 339, satellite 344, 347, sun 
seen from 422, surface of 369 

Newcomb, S., Prof. Johns Hopkins Univ. 
4, 128, 143, 167, 221, 362, 427 

Newton, H. A. (1830-96), Am. ast. 412 

Newton, Sir I. (1643 -1727), Eng. ast. 80, 191, 
197, 199, 247, 371-91. 393, 471 

Newtonian, law 329, 380, telescope 203, 205 

Nice (nece), Observatory of 202 

Nickel in sun 276 

Night {see Day) 100, at equator 103, at the 
equinoxes loi, at solstices 102, long polar 
107, south of equator 103 

Nitrogen, in comets 406, not in sun 277 

Nodes, moon's 231, 293, planetary 324, 341, 342 

Noon (mean), iii, sidereal time of 121 

Norma, Plate iv. 62, new star in 448, 449 

North, finding true 115 

North polar distance defined 51 

North polar heavens, Plate in. 60 

Notation, Eng. system of 41, Fr. 40 

Nutation, cause of 391, defined 390 

Oberon (o'ber-on), satellite of Uranus 347 
Objective 195, achromatic 198, efficiency 199 
Obliquity of ecliptic 150 
Observatories 190, best sites 191 
Occlusion of gases 420 
Occultations 310, Jupiter's satellites 345 
Oceanus. river of mythology 76 
Olbers, H. W. M. (1758-1840), Ger. ast. 362 
Omicron (o-mi'kron), Ceti variables 445, 446 
Ophiuchus (oph-i-u'kus), Kepler's star in 447 
Opposition of planets 317 
Orbit, earth's 133, 136, 139, 140 
Orbits (planetary) 322, elements 329, experi- 
mental 378, secular variations 140, 330 
Ori'on, Plate iv. 62, 430 
Orionids, meteors 414 
Oxygen in sun 277 

Palisa, J. (pa-le'sa), ast. Vienna Obs. 362 
Pallas, small planet 335 
Pantheon (pon-ta-awng), Paris 99 
Parabola, comet orbit 397, 398 
Parallactic ellipse, star's 436 
Parallax, annual 435, moon's 235, sun's 258 
Paris, INIuseum, meteorites 412, Observatory 
57, 123, 205, 217, 248, 249, 282 



478 



Index 



Paschal moon i68 

Paul, H. M., Prof. U. S. Navy 450 

Payne, W. W., Dir. Carleton Col. Obs. 401, 

446 
Pegasus, Square of, Plate iv. 62, 66 
Peirce, C. S. (purse), Am. geom. 89 
Pendulums 88, 2x2 
Periastron defined, 453 
Perigee, moon's 233 
Perihelion defined 139 
Perpetual apparition and occultation 71 
Perrotin, J. (pehr-ro-tang'), Dir. Nice Obs. 

Perseids, meteors 414, 417 

Perseus (per'suce) Plate in. 60, Plate iv. 62, 
cluster in 457, 458 

Personal equation 214, machine 215 

Petavius, D. (1583-1652), Fr. chronologist 247 

Peters, C. H. F. (1813-90), Am. ast. 362 

Phoenix, Plate iv. 62 

Photo-chronograph 214 

Photography, celestial 218, 365-7, discoveries 
by 220, 457, of moon 16, 248, of nebulae 
460-3, of planets 365, 366, of stars 13, 458, 
(spectra) 434, 443, of sim 264, 269, 281-3 

Photometer 194 

Photosphere, solar 264, 284 

Piazzi, G. (pe-at'si) (1746-1826), It. ast. 361 

Picard, J. (pe-car') (1620-82), Fr. geom. 80, 
190 

Pickering, E. C, Dir. Harv. Co-ll. Obs. 4, 219, 
423, 443-5, 448, 449> 455; W. H., Prof. 
Harv. Univ. 346, 359, 360, 464 

Pigott, E. (1768-1807), Eng. ast. 401 

Pilatre de Rozier, J. F. (pee-lottr' diih-ro- 
_ze-a') (1756-85), Fr. aeronaut 291 

Pisces, Plate iv. 62 

Piscis Australis, Plate iv. 62 

Planetary system, evolution of 466, 467 

Planets {^see also Jupiter, Mars, Mercury, 
Neptune, Saturn, Uranus, Venus) 17, 311, 
albedo 332, apparent motions 311, apparent 
size 331, aspects 315, atmospheres 348, axial 
inclination 337, classifications of 314, colors 
332, configurations 315, 317, conjunction 315, 
densities 335, different from stars 18, dimen- 
sions 334, distances 325, 327, 333, eccentric- 
ity 324, elements 329, ellipticity 337, elonga- 
tion 316, evolution of 467, exterior 314, 315, 
exterior to Neptune 370, farthest planet 328, 
heliocentric movements 322, 323, inclination 
324, interior 314, 315, intramercurian 314, 
libration 337, loop of path 319, major 314, 
323, masses 335, mass found (by satellite) 
384, (without satellite) 385, measuring diame- 
ter 209, minor 314, motion (in epicycle) 312, 
(laws of) 326, (retrograde) 319, naked-eye 
appearance 313, nearest 328, nodes 324, op- 
position 317, orbits 322, 323, periods 325, 
326, phases 318, quadrature 317, rotation 336, 
satellites 343, secular variations 140, 330, 
small 314, 361, 362, surfaces of 350, terres- 
trial 314, 321, transits of inferior 339 

Plato (B.C. 390), Gk. phil. 76, 247 

Pleiades (ple'ya-deez) 129, 220, 237, 430, 444, 
456 

Plumb-line 23 

Poincare, H. (pwang-ka-ray'). Prof. Univ. 
Paris 470 

Polar axis 53 

Polaris 32, 60, Plate in. 62, 66, 69, 439, 441, 452 



Pole, celestial north, defined 35, finding the 33 
Poles, the wandering terrestrial 95 
Pollux O Geminorum), Plate iv. 62, 423, 441 
Pons, J. L. (1761-1831)', Fr. ast. 393, 394, 403 
Popular Astronomy (monthly) 357, 401, 446 
Porter, J. G., Dir. Cincinnati Obs. 430, 431 
Posidonius (b c. 260), Gk. phil. 80 
Pratt, H, (1838-91), Eng. ast. 366 
Precession, cause of 390, defined and illus- 
trated 128, effects of 129, 426, explanation 
of period of 128, planetary 390 
Preston, E. D., U. S. Coast Survey 89, 96 
Prime vertical, defined 28, 58 
Prmcipia, Newton's 372 
Pritchard, C. (1808-93), Eng. ast. 437 
Pritchett, C. W., Dir. Glasg. Obs. 364; H. S.. 

Supt. tJ. S. Coast and Geod. Surv. 302 
Proclus (a.d. 450), Gk phil. 247 
Proctor, R. A. (1837-88), Am. ast. 64, 430, 

464 
Procyon, Plate iv. 62, 423, 425, 439, 441 
Prominences, Plate n. 11, 280-3, Plate v. 
Proper motions 429 
Ptolemaic system 313 
Ptolemy, C. (tol'e-m]) (a.d. 140), Alex. ast. 

81, 247, 313, 429 
Pulkowa (pul-ko'va) Obs. 202, 220, 455 
Pyrheliometer 194 
Pythagoras (b.c. 530), Gk. phil. 76, 392 

Quadrantids, meteors 414 
(Quadrature, moon's 223, planets' 317 
Quenisset, F. (kay-nis'say), Fr. ast. 397 
Quit, sun's 431 

Radian, angular unit 46 

Radiant, meteoric 413 

Radius vector, defined 137, 139 

Ramsay, W., Prof. Univ. Col. London 280 

Ramsden, J. (1735-1800), Eng. opt. 207 

Ranyard, A. C. (1845-94), Eng. ast. 440 

Rayet, M. (ry-a'), Univ. Bordeaux 443 

Rees, J. K., Dir. Columb. Univ. Obs. 96 

Reflectors 193, 203, 205 

Refraction, atmospheric 90-2 

Refractors 193, 196, 202, 205 

Regulus (a Leonis), Plate iv. 62, 423, 441 

Repsold, A., Ger. instrument maker 202 

Reticles 210, 211 

Reversing layer 284, 298, 302 

Rhea, satellite of Saturn 346 

Riccioli, G. B. (rit-se-o'le) (1598-1671), It. 

ast. 249 
Richaud, M. (re-show') (1650-1700), Fr. ast. 

453 
Richer, J. (re-shay') (1640-96), Fr. ast. 88 
Rigel O Orionis), Plate iv. 62, 423, 434, 452 
Right ascension, defined 51, 58 
Ritchie, J., Am. ast. 362 
Roberts, I., Eng. ast. 4, 457, 458, 460-3 
Roche, E. A. (roash) (1820-80), Fr. math. 469 
Roemer, O. (reh'mer) (1644-1716), Danish 

ast. 210, 345 
Rogers, W. A., Prof. Colby Univ. 64 
Rordame, A., Am. ast. 397 
Rosse, Lord (1800-67), Brit. ast. 205, 462, 468 
Rowland, H. A. (ro'land). Prof. Johns Hop- 
kins Univ. 191, 274, 276 
Runge, K. (roong'eh) Ger. physicist 277 
Russell, H. C, Govt. ast. Sydney 365, 459, 
461 



Index 



479 



Saegmiiller, G. N. (seg'miller) 215 

Safford, T. H., Dir. Wms. Col. Obs. 427 

Sagittarius, Plate iv. 62 

Saros, cycle of eclipses 309 

Saturn 18, albedo 333, atmosphere 349, axial 
inclination 337, color 332, configurations 317, 
density 336, diameter 334, distance 328, 
drawings 18, 366, 367, eccentricity 324, 
ellipticity 337, inclination 324, libration 338, 
loop in path 319, mass 335, 385, naked-eye 
appearance 313, orbit 323, periods 325, 326, 
phase 319, photographs 366, polar flattening 
367, retrograde motion 320, rotation 336, 
339, satellites of 346, 347, surface of 366 

Sawyer, E F., Am. ast. 446 

Schaeberle, J. M. (sheb'bur-ly), ast. Lick 
Obs. 300, 408 

Scheiner, J., ast. Potsdam Obs. 445 

Schiaparelli, G.V. (skap-pa-rell'ly), Dir. Roy. 
Obs. Milan 358, 359 

Schickard, W. (1592-1635), Ger. math. 247 

Schiehallion, Mt., in Scotland 90 

Schiller, J. C. F. (1759-1805), Ger. poet 247 

Scbjellerup, H. C. F. C. (1827-87), Danish 
ast. 442 

Schuster, A., Prof. Victoria Univ. 301, 408 

Scintillation of stars 44, 92 

Scorpio, Plate iv. 62, new star in 447 

Sculptor, Plate iv. 62 

Seasons 152, 154, 159, 160 

Secchi, A. (seck'key) (1818-78), It. ast. 265, 
441-4 

Secular variations 140, 330 

See, T. J. J., Lowell Obs. 354, 452, 454, 469 

Serpens, Plate iv. 62 

Serviss, G. P., Am. ast. 64 

Sextans, Plate iv. 62 

Sextant 181, adjustments 181 

Shadows of heavenly bodies 291, 304, 306 

Shooting stars i^see Meteors) 411, 412 

Sidereal system 421 

Sidereal time of mean noon 121 

Sight, model 49, taking a 183 

Silicon in sun 276 

Silver in sun 276 

Sirian stars 441, 442 

Sirius, Plate iv. 62, 423, 426, 439, 440, 442, 453 

Slit, dome 192, spectroscope 275 

Snell, W. (1591-1626), Dutch math. 81 

Sodium, in comets 406, in sun 276 

Solar constant 286 

Solar disk, the winged 255 

Solar eclipses 290-8 

Solar stars 441, 442 

Solar system, described 315, evolution of 466 

Solis Lacus on Mars 358 

Solstices 37, 57, 147, 149 

Sosig'enes (b.c. 50), Alex. ast. 166 

Southern Cross visible 184 

Space, infinite 471 

Spectral image test 201 

Spectro-bolometer 278 

Spectro-heliograms 269, 282, 283 

Spectro-heliograph 270, 280. 281 

Spectroscopes 193, 271-4 

Spectrum, discontinuous 272, normal 273, 
stellar 441-5, 448 

Spectrum analysis 271, 273, 275, 470 

Speculum 204 

Sphere, armillary 29, celestial 27, 43, 58, par- 
allel 70, right 73, terrestrial 26 



Spica (a Virginis), Plate iv. 62, 423, 434 

Spitaler, R., ast. Prague Obs. 401 

Spoerer, F. W. G. (1822-95), Ger. ast. 268 

Spring in general 153, months of 159 

Stadium 80 

Standard time, 124, 125, 186, 188 

Stars 421, are suns 19, 422, binary {see Binary 
stars), brightest 423, brightness related to dis- 
tance 434, by night 11, catalogues and charts 
60 -3, 426, circumpolar 32, 61, colors 425, con- 
stellations 14, 59, 430, constitution 426, 441-3, 
445, 448, dark 450, 453, dimensions 440, 
distances 439, 440, distances, how found 435, 
distances illustrated ig, 437, distribution of 
459, double {see Double stars), grouping 
456, 459, Herschel's gauges 460, in their 
courses 59, light from 424, magnitudes of 
60, 422, motion in line of sight 431, 434, 
multiple 451, 456, new 444, 447, 448, num- 
ber of 12, 14, 424, parallaxes 435-40, planets 
belonging to 19, proper motions 429, quad- 
ruple 451, 456, runaway 430, secular changes 
430, spectra 441-5, 448, 470, standard 426, 
streams of 459, telling time by, 109, tempo- 
rary 444, 447, 448, triple 451, 456, twinkling 
of 44, 92, variable {see Variable stars), visi- 
ble in daytime 11 

Star trails 33, 34, 216 

Steinheil, R. (styn'hile), Ger. opt. 202 

Stone, O., Dir. Obs. L^niv. Va. 465 

Struve, F. G. W. (stroo'vuh) (1793-1864), 
Ger.-Russ. ast. 451; H., Dir. Obs. Kbnigs- 
berg, 346; L., Dir. Kharkov Obs. 431 

V. Struve, O. W., Ger.-Russ. ast. 451 

Summer in general 153, months of 159 

Sumner, T. H. (1810-70), Am. navigator 183 

Sumner's method 183 

Sun 255, absorption by its atmosphere 279, 
apparent annual motion 132, 146, brilliance 
of 285, calcium in 270, central 431, chromo- 
sphere 280, 284, constitution 276, 283, con- 
traction of 287, declination of 85, density 
262, dimensions 259, 260, distance of 143, 
258, distance (illustrated) 141, (a unit) 257, 
eclipses of, froyit., 289-305, elements in 
276, envelopes of 283, evolution of 466, 
faculse 264, 269, 270, fictitious in, gravity 
at surface 262, heat of 286, its duration 469, 
light of 285, maintenance 287, 470, mass 
262, 386, metals in 276, midsummer highest 
30, 148, midwinter 147, observing the 263, 
overhead at noon 184, parallax 258, past 
and future of 288, photosphere 264, 284, 
prominences, Plate 11. 11, 280, 282,283, rays 
at equinox and solstice 146, reversing layer 
284, 298, 302, rice grains 264, rotation 270, 
ruler 255, secular motion 431, solar con- 
stant 286, spectrum 275, 276-8, spherical 
261, spots II, 265-9, spot spectrum 277, 
stellar magnitude 423, strength of attraction 
383, temperature 287, veiled spots 265, vol- 
ume 262, ' way* (apex) 431 

Sundial 115 

Sunrise and sunset 104, 105, 113 

Survey, gravimetric 88, U. S. Coast & Geod. 
80, 176 

Swe'denborg, E. (1688-1772), Swed. phil. 
468 

Swift, L., Am. ast. 393, 401, 461 

Symbols, usual astronomical 40 

Syzygy, moon's 232 



48o 



Index 



Tacchini, P. (tock-kee'nee), Dir. Obs. Col. 
Rom. 283 

Taurus, Plate iv. 62 

Taylor, H. D., Eng. opt. 199 

Telescopes, achromatic 198, 199, astronomy 
before 190, classified 193, early 197, equa- 
torial 52, great future 204, invention 190, 
196, 203, kinds of 195, making a small 201, 
mistakes about 218, reflectors (q.v.), re- 
fractors (qv), testing 200, tube 195 

Telespectroscope 274 

Telluric lines 276, 279 

Tempel, E. W. L. (1821-89) , Ger. ast. 393, 401 

Terminator, moon's 222 

Tethys (teth'iz), satellite of Saturn 346 

Tewfik (tefif'ik) (1852-92), Egyp. khedive 408 

Thales (b c. 600), Gr. phil. 76, 289 

Thermopile 194 

Thulis, M. (tu-lee') (1750-1805), Fr. ast. 394 

Tidal, bore 179, evolution 338, friction 469 

Tides 174-9, explained by gravitation 387 

Time 9, all over the v^orld 127, apparent no, 
distribution of 125, equation of 112 (ex- 
plained), 150, mean no, measurement of 
115-23, observatory 119, ship's 173, sidereal 
and solar 120, signals 186, 187, standard 124, 
125, sundial 115, telling by the stars 109 

Time ball 9, 125, 186, 187 

Tisserand, F. F. (1845-96), Fr. ast. 4 

Titan, satellite of Saturn 346, 347, 366 

Titania, satellite of Uranus 347 

Titius, J. D. (1729-96), Ger. math. 333 

Transit instrument 209, 210, adjusting 210, 
room 193, rudimentary 117 

Transits of inferior planets 339 

Transneptunian planets 370 

Triangle transit 119 

Triangulation defined 81, 257 

Triangulum, Plate iv. 62 

Triesnecker, crater 247, 251, 253 

Trouvelot, L (troo've-lo) (1820-92) 11, 284 

Trow^bridge, M. L., photographer 45 

Turner, H. H., Dir. Oxford Univ. Obs. 446 

Tuttle, H. P. (1839-92), Am. ast. 401 

Tw^ilight 93 

Twinkling of stars 44, 92 

Tycho Brahe (1546-1601), Danish ast. 57,247, 
393» 447 

Ulugh-Beg (1394-1449), Arab. ast. 427 

Umbriel, satellite of Uranus 347 

Unit, angular 46, of celestial distance 141, 438 

U.S., National Museum, meteorites 412, 418, 
Naval Obs. 202 

Universe, stellar 421, other universes 470 

Upton, W., Dir. Brown Univ. Obs. 64 

Uraninite 280 

Uranus (yew'ra-nus), albedo 333, atmosphere 
350, color 332, configurations 317, density 
336, diameter 334, discovery of 369, distance 
328, drawings 370, eccentricity 324, ellip- 
ticity 337, loop in path 319, mass 335, me- 
teors near 415, naked eye appearance 314, 
orbit 323, periods 325, 326, relative distance 



and motion 333, retrograde motion 320, rota- 
tion 337, 339, satellites 344, 347, surface 369 

Ursa Major, Plate iv 62, 116, 430 

Ursa Minor, Plate ni. 60 

Variable stars 445, algol 449, causes 450, dis- 
tribution 446, irregular 449, observing 446 

Vega 31, Plate in. 60, 130, 423, 431, 439, 444 

Venus 18, albedo 332, atmosphere 348, chart 
of 354, color 332, conjunctions 315, density 
335, diameter 334, distance 328, drawings 
3535 354, eccentricity 325, greatest brilliancy 
315, greatest elongation 316, illuminated 
hemisphere 353, inclination 324, mass 335, 
naked-eye appearance 313, nearest planet 
328, orbit 322, periods 325, 326, phase 318, 
331, relative distance and motion 333, retro- 
grade motion 319, rotation 337, 339, sup- 
posed satellite 343, transits 340, 342, 348, 
variation in size 331 

Vertical circle, defined 28, 58 

Very, F. W., Am. ast. 245 

Vesta 314, 335, 361 

Vienna, meteorites 412, 418 

Virgo, Plate iv. 62 

Vogel, H., Dir. Obs. Potsdam 434, 443, 445 

Vulpecula, Plate iv. 62 

Walther (1430-1504), Ger. ast. 247 

Warner & Swasey 15, 54, 86, 202, 213 

Washington, meridian of 123 

Watson, J. C. (1838-80), Am. ast. 362 

Webb, T. W. (1807-85), Eng. ast. 64 

Week, origin of days of 166 

Wesley, W. H., Libr. Roy. Ast. Soc. 301 

Widmannstatian (vid-mon-stet'yan) figs. 419 

Williams, A. S., Eng. ast. 359, 366 

Wilson, H. C., Prof. Carleton Col. 359, 407 

Winged globe 255 

Winter in general 153, months of 159 

Wolf, C, Prof. Univ. Paris 443; M., Prof. 

Univ. Heidelberg 362, 411, 459; R. (1816- 

93), Ger. ast. 401 
Wolfer, A., Dir. Obs. Zurich 269 
Wollaston, W. H. (1766-1828), Eng. physicist 

191 
Wood, R. W., Univ. Wisconsin 378 
Wright, T. (1711-86), Eng. phil. 468 

Yale University, meteorites, 412, 418 

Year, anomalistic 165, sidereal 165, tropical 

165 
Yerkes, C. T. (yer'kez), Am. patron, Ob- 
servatory 15, 200, 205, 432, telescope 15, 202, 

424 ^ 
Young, C. A., Dir. Princeton Obs. 270, 281, 
282, 298 

Zenith defined 24, 58; — distance defined 48 

Zenith telescope 85 

Zinc in sun 276 

Zodiac, 64-5, signs of 40 

Zodiacal light 315, 350 

Zones, Spoerer's law of 268, terrestrial 160 



Typography by J. S. Gushing & Co., Norwood, Mass., U.S.A. 



A. 



/v 



